0^" 


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SMITHSONIAN  INSTITUTION 

BUREAU  OF  AMERICAN  ETHNOLOGY 

BULLETIN  57 


AI  miRODUCTIO]^  TO  THE  STUDY 
OF  THE  MAYA  HIEROGLYPHS 


BY 

SYLVANUS  GRISWOLD  MORLEY 


WASHINGTON 
GOVERNMENT  PRINTING  OFFICE 
1915 


LETTER  OF  TRANSMITTAL 


Smitilsonian  Institution, 
Bureau  of  American  Ethnology, 

WasJiington,  D.  C,  January  7,  lOlJf.. 
Sir:  I  have  the  honor  to  submit  the  accompanying  manuscript  of 
a  memoir  bearing  the  title  ^^An  Introduction  to  the  Study  of  tlie 
Maya  Hieroglyphs/'  by  Sylvanus  Griswold  Morley,  and  to  recom- 
mend its  publication  as  a  bulletin  of  the  Bureau  of  American  Eth- 
nology. 

The  hieroglyphic  writing  developed  by  the  Maya  of  C^entral  America 
and  southern  Mexico  was  probably  the  foremost  intellectual  achieve- 
ment of  pre-Columbian  times  in  the  New  World,  and  as  such  it  de- 
serves equal  attention  with  other  graphic  systems  of  antiquity. 

The  earliest  inscriptions  now  extant  probably  date  from  about 
the  beginning  of  the  Christian  era,  but  such  is  the  complexity  of  the 
glyphs  and  subject  matter  even  at  this  early  period,  that  in  order  to 
estimate  the  age  of  the  system  it  is  necessary  to  postulate  a  far  greater 
antiquity  for  its  origin.  Indeed  aU  that  can  be  accepted  safely  in 
this  direction  is  that  many  centuries  must  have  elapsed  l)efore  the 
Maya  hieroglyphic  writing  could  have  been  developed  to  the  highly 
complex  stage  where  we  first  encounter  it. 

The  first  student  to  make  any  progress  in  deciphering  the  Maya 
inscriptions  was  Prof.  Ernst  Forstemann,  of  the  Royal  Library  at 
Dresden.  About  1880  Professor  Forstemann  published  a  facsimile 
reproduction  of  the  Dresden  codex,  and  for  the  next  twenty  years 
devoted  the  greater  part  of  his  time  to  the  elucidation  of  this  manu- 
script. He  it  was  who  first  discovered  and  worked  out  the  ingenious 
vigesimal  system  of  numeration  used  by  the  Maya,  and  who  first 
pointed  out  how  this  system  was  utilized  to  record  astronomical  and 
chronological  facts.  In  short,  his  pioneer  work  made  possible  aU 
subsequent  progress  in  deciphering  Maya  texts. 

Curiously  enough,  about  the  same  time,  or  a  little  later  (in  1891), 
another  student  of  the  same  subject,  Mr.  J.  T.  Goodman,  of  Alameda, 
California,  working  independently  and  without  knowledge  of  Pro- 
fessor Forstemann's  researches,  also  succeeded  in  deciphering  the 
chronological  parts  of  the  Maya  texts,  and  in  determining  the  values 
of  the  head-variant  numerals.    Mr.  Goodman  also  perfected  some 

in 


IV 


LETTER  OF  TRANSMITTAL 


tables,  ''The  Archaic  Chronological  Calendar"  and  "The  Archaic 
Annual  Calendar,"  which  greatly  facilitate  the  decipherment  of  the 
calculations  recorded  in  the  texts. 

It  must  be  admitted  that  very  little  progress  has  been  made  in 
deciphering  the  Maya  glyphs  except  those  relating  to  the  calendar  and 
chronology;  that  is,  the  signs  for  the  various  time  periods  (days  and 
months),  the  numerals,  and  a  few  name-glyphs;  however,  as  these 
known  signs  comprise  possibly  two-fifths  of  all  the  glyphs,  it  is  clear 
that  the  general  tenor  of  the  Maya  inscriptions  is  no  longer  concealed 
from  us.  The  remaining  three-fifths  probably  tell  the  nature  of  the 
events  which  occurred  on  the  corresponding  dates,  and  it  is  to  these 
we  must  turn  for  the  subject  matter  of  Maya  history.  The  deci- 
phering of  this  textual  residuum  is  enormously  complicated  by  the 
character  of  the  Maya  glyphs,  which  for  the  greater  part  are  ideo- 
graphic rather  than  phonetic;  that  is,  the  various  symbols  represent 
ideas  rather  than  sounds. 

In  a  graphic  system  composed  largely  of  ideographic  elements  it 
is  extremely  difficult  to  determine  the  meanings  of  the  different  signs, 
since  little  or  no  help  is  to  be  derived  from  varying  combinations  of 
elements  as  in  a  phonetic  system.  In  phonetic  writing  the  symbols 
have  fixed  sounds,  which  are  unchanging  throughout,  and  when  these 
values  have  once  been  determined,  they  may  be  substituted  for  the 
characters  wherever  they  occur,  and  thus  words  are  formed. 

While  the  Maya  glyphs  largely  represent  ideas,  indubitable  traces 
of  phoneticism  and  phonetic  composition  appear.  There  are  per- 
haps half  a  dozen  glyphs  in  all  which  are  known  to  be  constructed 
on  a  purely  phonetic  basis,  and  as  the  remaining  glyphs  are  gradually 
deciphered  this  number  will  doubtless  be  increased. 

.The  progress  which  has  been  made  in  deciphering  the  Maya  inscrip- 
tions may  be  summarized  as  f oUows :  The  Maya  calendar,  chronology, 
and  astronomy  as  recorded  in  the  hieroglyphic  texts  have  been  care- 
fully worked  out,  and  it  is  unlikely  that  future  discoveries  will  change 
our  present  conception  of  them.  There  remains,  however,  a  group  of 
glyphs  which  are  probably  non-calendric,  non-chronologic,  and  non- 
astronomic  in  character.  These,  it  may  be  reasonably  expected, 
will  be  found  to  describe  the  subject  matter  of  Maya  history;  that  is, 
they  probably  set  forth  the  nature  of  the  events  which  took  place  on 
the  dates  recorded.  An  analogy  would  be  the  following:  Supposing, 
in  scanning  a  history  of  the  United  States,  only  the  dates  could  be 
read.  We  would  find,  for  example,  July  4,  1 776,  followed  by  unknown 
characters;  April  12,  1861,  by  others;  and  March  4,  1912,  by  others. 
This,  then,  is  the  case  with  the  Maya  glyphs — we  find  dates  followed 
by  glyphs  of  unknown  meaning,  which  presumably  set  forth  the 
nature  of  the  corresponding  events.    In  a  word,  we  know  now  the 


LETTER  OF  TRANSMITTAL 


V 


chronologic  skeleton  of  Maya  history;  it  remains  to  work  out  the 
more  intimate  details  which  alone  can  make  it  a  vital  force. 

The  published  writings  on  the  subject  of  the  Maya  hieroglyphs  have 
become  so  voluminous,  and  are  so  widely  scattered  and  inaccessible, 
that  it  is  difficult  for  students  of  Central  American  archeology  to 
become  famihar  with  what  has  been  accomplished  in  this  important 
field  of  investigation.  In  the  present  memoir  Mr.  Morley,  who  has 
devoted  a  number  of  years  to  the  study  of  Maya  archeology,  and 
especiaUy  to  the  hieroglyphs,  summarizes  the  results  of  these  re- 
searches to  the  present  time,  and  it  is  believed  that  this  Introduction 
to  tJie  Study  of  the  Maya  Hieroglyphs  wiU  be  the  means  of  enabling 
ready  and  closer  acquaintance  with  this  interesting  though  intricate 
subject. 

Very  respectfully, 

F.  W.  Hodge, 
Ethnologist-in-  Charge . 

Dr.  Charles  D.  Walcott, 

Secretary  of  the  Smithsonian  Institution j 

Washington,  D,  0, 


PREFACE 


With  the  great  expansion  of  interest  in  American  archeology  during 
the  last  few  years  there  has  grown  to  be  a  corresponding  need  and 
demand  for  primary  textbooks,  archeological  primers  so  to  speak, 
which  will  enable  the  general  reader,  without  previous  knowledge  of 
the  science,  to  understand  its  several  branches.  With  this  end  in 
view,  the  author  has  prepared  An  Introduction  to  the  Study  of  the 
Maya  Hieroglyphs. 

The  need  for  such  a  textbook  in  this  particular  field  is  suggested 
by  two  considerations:  (1)  The  writings  of  previous  investigators, 
having  been  designed  to  meet  the  needs  of  the  specialist  rather  than 
those  of  the  beginner,  are  for  the  greater  part  too  advanced  and 
technical  for  general  comprehension;  and  (2)  these  writings  are  scat- 
tered through  many  publications,  periodicals  as  well  as  books,  some 
in  foreign  languages,  and  almost  all  difficult  of  access  to  the  average 
reader. 

To  the  second  of  these  considerations,  however,  the  writings  of 
Mr.  C.  P.  Bowditch,  of  Boston,  Massachusetts,  offer  a  conspicuous 
exception,  particularly  his  final  contribution  to  this  subject,  entitled 
'^The  Numeration,  Calendar  Systems,  and  Astronomical  Knowledge 
of  the  Mayas,"  the  publication  of  which  in  1910  marked  the  dawn  of 
a  new  era  in  the  study  of  the  Maya  hieroglyphic  writing.  In  this 
work  Mr.  Bowditch  exhaustively  summarizes  all  previous  knowledge 
of  the  subject,  and  also  indicates  the  most  promising  lines  for  future 
investigation.  The  book  is  a  vast  storehouse  of  heretofore  scattered 
material,  now  gathered  together  for  the  first  time  and  presented  to 
the  student  in  a  readily  accessible  form.  Indeed^  so  thorough  is  its 
treatment,  the  result  of  many  years  of  intensive  study,  that  the 
writer  would  have  hesitated  to  bring  out  another  work,  necessarily 
covering  much  of  the  same  ground,  had  it  not  been  for  his  belief  that 
Mr.  Bowditch's  book  is  too  advanced  for  lay  comprehension.  The 
Maya  hieroglyphic  writing  is  exceedingly  intricate;  its  subject  matter 
is  complex  and  its  forms  irregular;  and  in  order  to  be  understood  it 
must  be  presented  in  a  very  elementary  way.  The  writer  believes  that 
this  primer  method  of  treatment  has  not  been  followed  in  the  publi- 
cation in  question  and,  furthermore,  that  the  omission  of  specimen 
texts,  which  would  give  the  student  practice  in  deciphering  the  glyphs, 
renders  it  too  technical  for  use  by  the  beginner. 

VII 


VIII 


PKEFACE 


Acknowledgment  should  be  made  here  to  Mr.  Bowditch  for  his 
courtesy  in  permitting  the  reproduction  of  a  number  of  drawings 
from  his  book,  the  examples  of  the  period,  day  and  month  glyphs 
figured  being  derived  almost  entirely  from  this  source;  and  in  a  larger 
sense  for  his  share  in  the  establishment  of  instruction  in  this  field  of 
research  at  Harvard  University  where  the  writer  first  took  up  these 
studies. 

In  the  limited  space  available  it  would  have  been  impossible  to 
present  a  detailed  picture  of  the  Maya  civilization,  nor  indeed  is  this 
essential  to  the  purpose  of  the  book.  It  has  been  thought  advisable, 
however,  to  precede  the  general  discussion  of  the  hieroglyphs  with  a 
brief  review  of  the  habitat,  history,  customs,  government,  and  religion 
of  the  ancient  Maya,  so  that  the  reader  may  gather  a  general  idea 
of  the  remarkable  people  whose  writing  and  calendar  he  is  about  to 
study. 


CONTENTS 


Page 


Chapter  T.  The  Maya   1 

Habitat     1 

History   2 

Manners  and  customs   7 

II,  The  Maya  hieroglyphic  writing   22 

III.  How  the  Maya  reckoned  time   37 

The  tonalamati,  or  260-day  period   41 

The  haab,  or  year  of  365  days   44 

The  Calendar  Round,  or  18,980-day  period   51 

The  Long  Count   60 

Initial  Series   63 

The  introducing  glyph   ■  64 

The  cycle  glyph   68 

The  katun  glyph   68 

The  tun  glyph   70 

The  uinal  glyph   70 

The  kin  glyph   72 

Secondary  Series   74 

Calendar-round  dates   76 

Period-ending  dates   77 

U  kahlay  katunob   79 

IV.  Maya  arithmetic   87 

Bar  and  dot  numerals   87 

Head-variant  numerals   96 

First  method  of  numeration   105 

Number  of  cycles  in  a  great  cycle   107 

Second  method  of  numeration   129 

First  step  in  solving  Maya  numbers   134 

Second  step  in  solving  Maya  numbers   135 

Third  step  in  solving  Maya  numbers   136 

Fourth  step  in  solving  Maya  numbers   138 

Fifth  step  in  solving  Maya  numbers   151 

V.  The  inscriptions   156 

Texts  recording  Initial  Series   157 

Texts  recording  Initial  Series  and  Secondary  Series   207 

Texts  recording  Period  Endings   222 

Texts  recording  Initial  Series,  Secondary  Series,  and  Period 

Endings   233 

Errors  in  the  originals   245 

VI.  The  codices  '   251 

Texts  recording  tonalamatls.    251 

Texts  recording  Initial  Series   266 

Texts  recording  Serpent  Numbers   273 

Texts  recording  Ascending  Series   276 

IX 


List  of  Tables 


Page 


Table  I.  The  twenty  Maya  day  names   37 

II.  Sequence  of  Maya  days   42 

III.  The  divisions  of  the  Maya  year   45 

IV.  Positions  of  days  at  the  end  of  a  year   48 

V.  Relative  positions  of  days  beginning  Maya  years   53 

VI.  Positions  of  days  in  divisions  of  Maya  year   55 

VII.  Positions  of  days  in  divisions  of  Maya  year  according  to. Maya  nota- 
tion  55 

VIII.  The  Maya  time-periods   62 

IX.  Sequence  of  katuns  in  u  kahlay  katunob   80 

X.  Characteristics  of  head-variant  numerals  0-19,  inclusive   103 

XI.  Sequence  of  twenty  consecutive  dates  in  the  month  Pop   Ill 

XII.  Comparison  of  the  two  methods  of  numeration   133 

XIII.  Values  of  higher  periods  in  terms  of  lowest,  in  inscriptions   135 

XIV.  Values  of  higher  periods  in  terms  of  lowest,  in  codices   135 

XV.  The  365  positions  in  the  Maya  year   141 

XVI.  80  Calendar  Rounds  expressed  in  Arabic  and  Maya  notation   143 

XVII.  Interrelationship  of  dates  on  Stelse  E,  F,  and  J  and  Zoomorph  G, 

Quirigua   239 

X 


ILLUSTRATIONS 


Page 


Plate    1.  The  Maya  territory,  showing  locations  of  principal  cities  (map)...  1 

2.  Diagram  showing  periods  of  occupancy  of  principal  southern  cities  .  15 

3.  Page  74  of  the  Dresden  Codex,  showing  the  end  of  the  world  (accord- 

ing to  Forstemann)   32 

4.  Diagram  showing  occurrence  of  dates  recorded  in  Cycle  9   35 

5.  Tonalamatl  wheel,  showing  sequence  of  the  260  differently  named 

days   43 

6.  Glyphs  representing  Initial  Series,  showing  use  of  bar  and  dot 

numerals  and  normal-form  period  glyphs   157 

7.  Glyphs  representing  Initial  Series,  showing  use  of  bar  and  dot 

numerals  and  head-variant  period  glyphs    167 

8.  Glyphs  representing  Initial  Series,  showing  use  of  bar  and  dot 

numerals  and  head-variant  period  glyphs   170 

9.  Glyphs  representing  Initial  Series,  showing  use  of  bar  and  dot 

numerals  and  head- variant  period  glyphs   176 

10.  Glyphs  representing  Initial  Series,  showing  use  of  bar  and  dot 

numerals  and  head-variant  period  glyphs — Stela  3,  Tikal..  ....  178 

11.  Glyphs  representing  Initial  .Series,  showing  use  of  bar  and  dot 

numerals  and  head-variant  period  glyphs — Stela  A  (east  side), 
Quirigua   179 

12.  Glyphs  representing  Initial  Series,  showing  use  of  head-variant 

numerals  and  period  glyphs   180 

13.  Oldest  Initial  Series  at  Copan — Stela  15   187 

14.  Initial  Series  on  Stela  D,  Copan,  showing  full-figure  numeral  glyphs 

and  period  glyphs   188 

15.  Initial  Series  on  Stela  J,  Copan   191 

16.  Initial  Series  and  Secondary  Series  on  Lintel  21,  Yaxchilan   207 

17.  Initial  Series  and  Secondary  Series  on  Stela  1,  Piedras  Negras   210 

18.  Initial  Series  and  Secondary  Series  on  Stela  K,  Quirigua   213 

19.  Initial  Series  and  Secondary  Series  on  Stela  F  (west  side),  Quirigua.  218 

20.  Initial  Series  on  Stela  F  (east  side),  Quirigua   220 

21.  Examples  of  Period-ending  dates  in  Cycle  9   223 

22.  Examples  of  Period-ending  dates  in  cycles  other  than  Cycle  9   227 

23.  Initial  Series,  Secondary  Series,  and  Period-ending  dates  on  Stela  3, 

Piedras  Negras   233 

24.  Initial  Series,  Secondary  Series,  and  Period-ending  dates  on  Stela  E 

(west  side),  Quirigua   235 

25.  Calendar-round  dates  on  Altar  5,  Tikal   240 

26.  Initial  Series  on  Stela  N,  Copan,  showing  error  in  month  coefficient..  248 

27.  Page  12  of  the  Dresden  Codex,  showing  tonalamatis  in  all  three 

divisions   254 

28.  Page  15  of  the  Dresden  Codex,  showing  tonalamatis  in  all  three 

divisions.   260 

29.  Middle  divisions  of  pages  10  and  11  of  the  Codex  Tro-Cortesiano, 

showing  one  tonalamatl  extending  across  the  two  pages   262 

30.  Page  102  of  the  Codex  Tro-Cortesiano,  showing  tonalamatis  in  the 

lower  three  divisions   263 

XI 


XII 


ILLUSTRATIONS 


Page 


Plate  31.  Page  24  of  the  Dresden  Codex,  showing  Initial  Series   266 

32.  Page  62  of  the  Dresden  Codex,  showing  the  Serpent  Numbers   273 

Figure  1.  Itzamna,  chief  deity  of  the  Maya  Pantheon   16 

2.  Kukulcan,  God  of  Learning   17 

3.  Ahpuch,  God  of  Death   17 

4.  The  God  of  War   17 

5.  Ek  Ahan,  the  Black  Captain,  war  deity    18 

6.  Yum  Kaax,  Lord  of  the  Harvest   18 

7.  Xaman  Ek,  the  North  Star  God   19 

8.  Conflict  between  the  Gods  of  Life  and  Death  (Kukulcan  and  Ah- 

puch)  19 

9.  Outlines  of  the  glyphs   22 

10.  Examples  of  glyph  elision,  showing  elimination  of  all  parts  except 

essential  element   23 

11.  Normal-form  and  head- variant  glyphs,  showing  retention  of  essen- 

tial element  in  each   24 

12.  Normal-form  and  head- variant  glyphs,  showing  absence  of  com- 

mon essential  element  -  -  25 

13.  Glyphs  built  up  on  a  phonetic  basis   28 

14.  A  rebus.    Aztec,  and  probably  Maya,  personal  and  place  names 

were  written  in  a  corresponding  manner   29 

15.  Aztec  place  names   30 

16.  The  day  signs  in  the  inscriptions   38 

17.  The  day  signs  in  the  codices    39 

18.  Sign  for  the  tonalamatl  (according  to  Goodman)   44 

19.  The  month  signs  in  the  inscriptions   49 

20.  The  month  signs  in  the  codices   50 

21.  Diagram  showing  engagement  of  tonalamatl  wheel  of  260  days 

and  haab  wheel  of  365  positions;  the  combination  of  the  two 

giving  the  Calendar  Round,  or  52-year  period   57 

22.  Signs  for  the  Calendar  Round   59 

23.  Diagram  showing  section  of  Calendar-round  wheel   64 

24.  Initial-series  "introducing  glyph"   65 

25.  Signs  for  the  cycle   68 

26.  Full-figure  variant  of  cycle  sign   69 

27.  Signs  for  the  katun   69 

28.  Full-figure  variant  of  katun  sign   70 

29.  Signs  for  the  tun   70 

30.  Full-figure  variant  of  tun  sign   70 

31.  Signs  for  the  uinal   71 

32.  Full-figure  variant  of  uinal  sign  on  Zoomorph  B,  Quirigua   71 

33.  Full-figure  variant  of  uinal  sign  on  Stela  D,  Copan   71 

34.  Signs  for  the  kin   72 

35.  Full-figure  variant  of  kin  sign   73 

36.  Period  glyphs,  from  widely  separated  sites  and  of  different  epochs, 

showing  persistence  of  essential  elements   74 

37.  Ending  signs  and  elements   78 

38.  "Snake"  or  "knot"  element  as  used  with  day  sign  Ahau,  possibly 

indicating  presence  of  the  u  kahlay  katunob  in  the  inscriptions.  83 

39.  Normal  forms  of  numerals  1  to  19,  inclusive,  in  the  codices   88 

40.  Normal  forms  of  numerals  1  to  19,  Inclusive,  in  the  inscriptions. . .  89 

41.  Examples  of  bar  and  dot  numeral  5,  showing  the  ornamentation 

which  the  bar  underwent  without  affecting  its  numerical  value. .  89 


ILLUSTEATIONS 


XIII 


Figure  42.  Examples  showing  the  way  in  which  numerals  1,  2,  6,  7,  11,  12,  16,  Page 
and  17  are  not  used  with  period,  day,  or  month  signs   90 

43.  Examples  showing  the  way  in  which  numerals  1,  2,  6,  7,  11,  12,  16, 

and  17  are  used  with  period ,  day,  or  month  signs   90 

44.  Normal  forms  of  numerals  1  to  13,  inclusive,  in  the  Books  of  Chilan 

Balam   9j 

45.  Sign  for  20  in  the  codices   92 

46.  Sign  for  0  in  the  codices   92 

47.  Sign  for  0  in  the  inscriptions   93 

48.  Figure  showing  possible  derivation  of  the  sign  for  0  in  the  inscrip- 

tions....... ,   93 

49.  Special  sign  for  0  used  exclusively  as  a  month  coefficient   94 

50.  Examples  of  the  use  of  bar  and  dot  numerals  with  period,  day,  or 

month  signs   95 

51.  Head-variant  numerals  1  to  7,  inclusive   97 

52.  Head-variant  numerals  8  to  13,  inclusive   98 

53.  Head-variant  numerals  14  to  19,  inclusive,  and  0   99 

54.  A  sign  for  0,  used  also  to  express  the  idea  "ending"  or  ''end  of" 

in  Period-ending  dates   102 

55.  Examples  of  the  use  of  head-variant  numerals  with  period,  day,  or 

month  signs   104 

56.  Examples  of  the  first  method  of  numeration,  used  almost  exclu- 

sively in  the  inscriptions   105 

57.  Signs  for  the  cycle  showing  coefficients  above  13   110 

58.  Part  of  the  inscription  on  Stela  N,  Copan,  showing  a  number  com- 

posed of  six  periods   II5 

59.  Part  of  the  inscription  in  the  Temple  of  the  Inscriptions,  Palenque, 

showing  a  number  composed  of  seven  periods   ]15 

60.  Part  of  the  inscription  on  Stela  10,  Tikal  (probably  an  Initial 

Series),  showing  a  number  composed  of  eight  periods   115 

61.  Signs  for  the  great  cycle  and  the  great-great  cycle   118 

62.  Glyphs  showing  misplacement  of  the  kin  coefficient  or  elimination 

of  a  period  glyph   128 

63.  Examples  of  the  second  method  of  numeration,  used  exclusively 

in  the  codices   131 

64.  Figure  showing  the  use  of  the  "minus "or  "backward"  sign  in  the 

codices   137 

65.  Sign -for  the  "month  indicator"   I53 

66.  Diagram  showing  the  method  of  designating  particular  glyphs  in  a 

text...   156 

67.  Signs  representing  the  hotun,  or  5-tun,  period   166 

68.  Initial  Series  showing  bar  and  dot  numerals  and  head-variant 

period  glyphs   I74 

69.  Initial  Series  showing  head-variant  numerals  and  period  glyphs. . .  183 

70.  Initial  Series  showing  head-variant  numerals  and  period  glyphs. . .  186 

71.  Initial  Series  on  Stela  H,  Quirigua   I93 

72.  The  tun,  uinal,  and  kin  coefficients  on  Stela  H,  Quirigua   194 

73.  The  Initial  Series  on  the  Tuxtla  Statuette,  the  oldest  Initial  Series 

known  (in  the  early  part  of  Cycle  8)   I95 

74.  The  introducing  glyph  (?)  of  the  Initial  Series  on  the  Tuxtla  Statu- 

ette  196 

75.  Drawings  of  the  Initial  Series:  A,  On  the  Leyden  Plate;  B,  on  a 

lintel  from  the  Temple  of  the  Initial  Series,  Chichen  Itza   197 


XIV 


ILLUSTRATIONS 


Page 


Figure  76.  The  Cycle-10  Initia-l  Series  from  Quen  Santo   200 

77.  Initial  Series  which  proceed  from  a  date  prior  to  4  Ahau  8  Climhu, 

the  starting  point  of  Maya  chronology   204 

78.  The  Initial  Series  on  Stela  J,  Qubigua   215 

79.  The  Secondary  Series  on  Stela  J,  Qiiirigua   216 

80.  Glyphs  which  may  disclose  the  nature  of  the  events  that  happened 

at  Quirigiia  on  the  dates:  a,  9.  14.  13.  4.  17  12  Caban  5  Kayab; 

6,  9.  15.  6.  14.  6  6Cimi  4Tzec   221 

81.  The  Initial  Series,  Secondary  Series,  and  Period-ending  date  on 

Altar  S,Copan   232 

82.  The  Initial  Series  on  Stela  E  (east  side),  Quirigua   236 

83.  Calendar-round  dates   241 

84.  Texts  showing  actual  errors  in  the  originals   245 

85.  Example  of  first  method  of  numeration  in  the  codices  (part  of  page 

69  of  the  Dresden  Codex)   275 


BIBLIOGRAPHY 


Aguilar,  Sanchez  de.  1639.  Informe  contra  idolomm  cultores  del  Obispado  de 
Yucatan.  Madrid.  (Reprint  in  Anales  Mus.  Nac.  de  Mexico,  vi,  pp.  17-122, 
Mexico,  1900.) 

BowDiTCH,  Charles  P.  1901  a.  Memoranda,  on  the  Maya  calendars  used  in  the 
Books  of  Chilan  Baiam.    Amer.  Anthr.,  n.  s.,  iii,  No.  1,  pp.  129-138,  New  York. 

  1906.    The  Temples  of  the  Cross,  of  the  Foliated  Cross,  and  of  the  Sun  at 

Palenque.    Cambridge,  Mass. 

  1909,  Dates  and  numbers  in  the  Dresden  Codex.  Putnam  Anniversary  Vol- 
ume, pp.  268-298,  New  York. 

 1910.    The  numeration,  calendar  systems,  and  astronomical  knowledge  of  the 

Mayas.    Cambridge,  Mass. 

Brasseur  de  Bofrbourg,  C.  E.  1869-70.  Manuscrit  Troano.  Etudes  sur  le 
systeme  grapliique  et  la  langue  des  Mayas.    2  vols.  Paris. 

Brinton,  Daniel  G.    1882  b.    The  Maya  chronicles.    Philadelphia.     (No.  1  of  ' 
Brinton's  Library  of  Aboriginal  American  Literature.) 

 1894  b.    A  primer  of  Mayan  hieroglyphics.    Pubs.  Univ.  of  Pa. ,  Ser.  in  Philol. , 

Lit.,  and  Archeol.,  iii,  No.  2. 

Bulletin  28  of  the  Bureau  of  American  Ethnology,  1904:  Mexican  and  Central 
American  antiquities,  calendar  systems,  and  history.  Twenty-four  papers  by 
Eduard  Seler,  E.  Forstemann,  Paul  Schellhas,  Carl  Sapper,  andE.  P.  Dieseldorff. 
Translated  from  the  German  under  the  supervision  of  Charles  P.  Bowditch. 

CoGOLLUDO,  D.  L.    1688.    Historia  de  Yucathan.  Madrid. 

Cresson,  H.  T.    1892.    The  antennae  and  sting  of  Yikilcab  as  components  in  the 

Maya  day-signs.    Science,  xx,  pp.  77-79,  New  York. 
DiESELDORFP,  E.  P.    See  Bulletin  28. 

Forstemann,  E.  1906.  Commentary  on  the  Maya  manuscript  in  the  Royal  Public 
Library  of  Dresden.  Papers  Peabody  Mus.,  iv.  No.  2,  pp.  48-266,  Cambridge. 
See  also  Bulletin  28. 

Gates,  W.  E.  1910.  Commentary  upon  the  Maya-Tzental  Perez  Codex,  with  a  con- 
cluding note  upon  the  linguistic  problem  of  the  Maya  glyphs.  Papers  Peabody 
Mus.,  VI,  No.  1,  pp.  5-64,  Cambridge. 

Goodman,  J.  T.  1897.  The  archaic  Maya  inscriptions.  (^Biologia  Centrali-Amori- 
cana,  Archaeology,  Part  xviii.    London.)    [^See  Maudslay,  1889-1902.] 

  1905.    Maya  dates.    Ainer.  Anthr.,  n.  s.,  vii,  pp.  642-647,  Lancaster,  Pa. 

Hewett,  Edgar  L.  1911.  Two  seasons'  work  in  Guatemala.  Bull.  Archxol.  Inst,  of 
America,  n,  pp.  117-134,  Norwood,  Mass. 

Holmes,  W.  H.  1907.  On  a  nephrite  statuette  from  San  Andres  Tuxtla,  Vera  Cruz, 
Mexico.    Amer.  Anthr.,  n.  s.,  ix,  No.  4,  pp.  691-701,  Lancaster,  Pa. 

Landa,  Diego  de.    1864.    Relacion  de  las  cosas  de  Yucatan.  Paris. 

Le  Plongeon,  A.  1885.  The  Maya  alphabet.  ^\i^p\Qm.eii\,  to  Scientific  American, 
vol.  XIX,  Jan.  31,  pp.  7572-73,  New,  York. 

Maler,  Teobert.  1901.  Researches  in  the  central  portion  of  the  Usumatsintla  val- 
ley.   Memoirs  Peabody  Mus.,  ii,  No.  1,  pp.  9-75,  Cambridge. 

  1903.  Researches  in  the  central  portion  of  the  Usumatsintla  valley.  [Contin- 
ued.]   Ibid.,  No.  2,  pp.  83-208. 

 : —  1908  a.    Explorations  of  the  upper  Usumatsintla  and  adjac-eiit  region.  Ibid., 

IV,  No.  1,  pp.  1-51. 

XV 


XVI 


BIBLIOGRAPHY 


Maler,  Teobert.    1908  b.    Explorations  in  the  Department  of  Peten,  Guatemala, 

and  adjacent  region.    Ibid.,  No.  2,  pp.  55-127. 
 1910.    Explorations  in  the  Department  of  Peten,  Guatemala,  and  adjacent 

region.    [Continued.]    Ibid.,  No.  3,  pp.  131-170. 
 1911.   Explorations  in  the  Department  of  Peten,  Guatemala.  Tikal.   Ibid.,  v, 

No.  1,  pp.  3-91,  pis.  1-26. 
Maudslay,  a.  p.    1889-1902.    Biologia  Centrali-Americana,  or  contributions  to  the 

knowledge  of  the  flora  and  fauna  of  Mexico  and  Central  America.  Archaeology. 

4  vols,  of  text  and  plates.  London. 
MoRLEY,  S.  G.   1910  b.   Correlation  of  Maya  and  Christian  chronology.   Amer.  Joum. 

ArcheoL,  2d  ser.,  xiv,  pp.  193-204,  Norwood,  Mass. 
 1911.    The  historical  value  of  the  Books  of  Chilan  Balam.    Ibid.,  xv,  pp. 

195-214. 

Ponce,  Fray  Alonzo.  1872.  Relacion  breve  y  verdadera  de  algunas  cosas  de  las 
muchas  que  sucedieron  al  Padre  Fray  Alonzo  Ponce,  Comisario  General  en  las 
provincias  de  Nueva  Espana.  Coleccion  de  documentos  ineditos  para  la  historia  de 
Espana,  lvii,  lviii.  Madrid. 

Rosny,  Leon  de.  1876.  Essai  sur  le  dechiffrement  de  I'ecriture  hieratique  de 
I'Amerique  Centrale.  Paris. 

Sapper,  Carl.    See  Bulletin  28. 

ScHELLHAS,  Paul.    See  Bulletin  28. 

Seler,  Eduard.  1901  c.  Die  alten  Ansiedelungen  von  Chacula  im  Distrikte  Nenton 
des  Departements  Iluehuetenango  der  Republik  Guatemala.  Berlin. 

  1902-1908.    Gesammelte  Abhandlungen  zur   amerikanischen   Sprach-  und 

Alterthumskunde.    3  vols.  Berlin. 
See  also  Bulletin  28. 

Spinden,  H.  J.  1913.  A  study  of  Maya  art,  its  subject-matter  and  historical  develop- 
ment.   Memoirs  Peabody  Mus.,  vi,  pp.  1-285,  Cambridge. 

Stephens,  J.  L.  1841.  Incidents  of  travel  in  Central  America,  Chiapas,  and  Yucatan. 
2  vols.    New  York. 

  1843.    Incidents  of  travel  in  Yucatan.    2  vols.    New  York. 

Thomas,  Cyrus.  1893.  Are  the  Maya  hieroglyphs  phonetic?  Amer.  Anthr.,  vi, 
No.  3,  pp.  241-270,  Washington. 

Villagutierre,  Sotomayor  J.  1701.  Historia  de  la  conquista  de  la  provinzia  de  el 
Itza,  reduccion,  y  progresses  de  la  de  el  Lacandon  y  otras  naciones  de  el  reyno  de 
Guatimala,  a  las  provincias  de  Yucatan,  en  la  America  septentrional.  Madrid. 


BUREAU  OF  AMERICAN  ETHNOLOGY 


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THE  MAYA  TERRITORY,   SHOWt^G   LOCATIONS  OF  PRINCIPAL  CITIES 


AN  INTRODUCTION  TO  THE  STUDY  OF  THE  MAYA  HIEROGLYPHS 

By  SYLVANUS  GRISWOLD  MORLEY 


Chapter  I.  THE  MAYA 


Habitat 


Broadly  speaking,  the  Maya  were  a  lowland  people,  inhabiting  the 
Atlantic  coast  plains  of  southern  Mexico  and  northern  Central  Amer- 
ica. (See  pi.  1.)  The  southern  part  of  this  region  is  abundantly 
watered  by  a  network  of  streams,  many  of  which  have  their  rise  in 
the  CordiUera,  while  the  northern  part,  comprising  the  peninsula  of 
Yucatan,  is  entirely  lacking  in  water  courses  and,  were  it  not  for 
natural  wells  (cenotes)  here  and  there,  would  be  uninhabitable.  This 
condition  in  the  north  is  due  to  the  geologic  formation  of  the  penin- 
sula, a  vast  plain  underlaid  by  limestone  through  which  water 
quickly  percolates  to  subterranean  channels. 

In  the  south  the  country  is  densely  forested,  though  occasional 
savannas  break  the  monotony  of  the  tropical  jungles.  The  roUing 
surface  is  traversed  in  places  by  ranges  of  hills,  the  most  important 
of  which  are  the  Cockscomb  Mountains  of  British  Honduras;  these 
attain  an  elevation  of  3,700  feet.  In  Yucatan  the  nature  of  the  soil 
and  the  water-supply  not  being  favorable  to  the  growth  of  a  luxuriant 
vegetation,  this  region  is  covered  with  a  smaller  forest  growth  and  a 
sparser  bush  than  the  area  farther  southward. 

The  chmate  of  the  region  occupied  by  the  Maya  is  tropical;  there 
are  two  seasons,  the  rainy  and  the  dry.  The  former  lasts  from  May 
or  June  until  January  or  February,  there  being  considerable  local 
variation  not  only  in  the  length  of  this  season  but  also  in  the  time  of 
its  beginning. 

Deer,  tapirs,  peccaries,  jaguars,  and  game  of  many  other  kinds 
abound  throughout  the  entire  region,  and  doubtless  formed  a  large 
part  of  the  food  supply  in  ancient  times,  though  formerly  corn  was 
the  staple,  as  it  is  now. 

There  are  at  present  upward  of  twenty  tribes  speaking  various 
dialects  of  the  Maya  language,  perhaps  haH  a  milUon  people  in  all. 
These  live  in  the  same  general  region  their  ancestors  occupied,  but 
under  greatly  changed  conditions.  Formerly  the  Maya  were  the  van 
of  civilization  in  the  New  World,^  but  to-day  they  are  a  dwindhng 

1  All  things  considered,  the  Maya  may  be  regarded  as  having  developed  probably  the  highest  aboriginal 
civilization  in  the  Western  Hemisphere,  although  it  should  be  borne  in  mind  that  they  were  surpassed  in 
many  lines  of  endeavor  by  other  races.  The  Inca,  for  example,  excelled  them  in  the  arts  of  weaving  and 
dyeing,  the  Chiriqui  in  metal  working,  and  the  Aztec  in  military  proficiency. 


1 


2 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


race,  their  once  remarkable  civilization  is  a  thing  of  the  past,  and  its 
manners  and  customs  are  forgotten. 

History 

The  ancient  Maya,  with  whom  this  volume  deals,  emerged  from  bar- 
barism probably  during  the  first  or  second  century  of  the  Christian 
Era;  at  least  their  earliest  dated  monument  can  not  be  ascribed  with 
safety  to  a  more  remote  period.^  How  long  a  time  had  been  required 
for  the  development  of  their  complex  calendar  and  hieroglyphic  sys- 
tem to  the  point  of  graphic  record,  it  is  impossible  to  say,  and  any 
estimate  can  be  only  conjectural.  It  is  certain,  however,  that  a  long 
interval  must  have  elapsed  from  the  first  crude  and  unrelated  scratches 
of  savagery  to  the  elaborate  and  involved  hieroglyphs  found  on  the 
earliest  monuments,  which  represent  not  only  the  work  of  highly 
skilled  sculptors,  but  also  the  thought  of  intensively  developed  minds. 
That  this  period  was  measured  by  centuries  rather  than  by  decades 
seems  probable;  the  achievement  was  far  too  great  to  have  been  per- 
formed in  a  single  generation  or  even  in  five  or  ten. 

It  seems  safe  to  assume,  therefore,  that  by  the  end  of  the  second 
century  of  the  Christian  Era  the  Maya  civilization  was  fairly  on  its 
feet.  There  then  began  an  extraordinary  development  all  along  the 
line.  City  after  city  sprang  into  prominence  throughout  the  southern 
part  of  the  Maya  territory,^  each  contributing  its  share  to  the  general 
progress  and  art  of  the  time.  With  accomphshment  came  confidence 
and  a  quickening  of  pace.  All  activities  doubtless  shared  in  the  gen- 
eral uphft  which  followed,  though  httle  more  than  the  material  evi- 
dences of  architecture  and  sculpture  have  survived  the  ravages  of  the 
destructive  environment  in  which  this  culture  flourished;  and  it  is 
chiefly  from  these  remnants  of  ancient  Maya  art  that  the  record  of 
progress  has  been  partially  reconstructed. 

This  period  of  development,  which  lasted  upward  of  400  years, 
or  until  about  the  close  of  the  sixth  century,  may  be  called  per- 

1  The  correlation  of  M&ya  and  Christian  chronology  herein  followed  is  that  suggested  by  the  writer  in 
"The  Correlation  of  Maya  and  Christian  Chronology"  {Papers  of  the  School  of  American  Archaeology,  No.  11). 
See  Morley,  1910  b,  cited  in  Bibliography,  pp.  xv,  xvi.  There  are  at  least  six  other  systems  of  correla- 
tion, however,  on  w^hich  the  student  must  pass  judgment.  Although  no  two  of  these  agree,  all  are  based 
on  data  derived  from  the  same  source,  namely,  the  Books  of  Chilan  Balam  (see  p.  3,  footnote  1).  The 
differences  among  them  are  due  to  the  varyiug  interpretations  of  the  material  therein  presented.  Some 
of  the  systems  of  correlation  which  have  been  proposed,  besides  that  of  the  writer,  are: 

1.  That  of  Mr.  C.  P.  Bowditch  (1901  a),  found  in  his  pamphlet  entitled  "Memoranda  on  the  Maya  Calen- 
dars used  in  The  Books  of  Chilan  Balam." 

2.  That  of  Prof.  Eduard  Seler  (1902-1908:  I,  pp.  588-599).   See  also  Bulletin  28,  p.  330. 

3.  That  of  Mr.  J.  T.  Goodman  (1905). 

4.  That  of  Pio  Perez,  in  Stephen's  Incidents  of  Travel  in  Yucatan  (1843:  i,  pp.  434-459;  n,  pp.  465-469) 
and  in  Landa,  1864:  pp.  366-429. 

As  before  noted,  these  correlations  differ  greatly  from  one  another.  Professor  Seler  assigning  the  most 
remote  dates  to  the  southern  cities  and  Mr.  Goodman  the  most  recent.  The  correlations  of  Mr.  Bowditch 
and  the  writer  are  within  260  years  of  each  other.  Before  accepting  any  one  of  the  systems  of  correlation 
above  mentioned,  the  student  is  strongly  urged  to  examine  with  care  The  Books  of  Chilan  Balam. 

2  It  is  probable  that  at  this  early  date  Yucatan  had  not  been  discovered,  or  at  least  not  colonized. 


MORLBY]      INTRODUCTION"  TO  STUDY  OF  MAYA  HIEROGLYPHS 


3 


haps  the  ''Golden  Age  of  the  Maya'';  at  least  it  was  the  first  great 
epoch  in  their  history,  and  so  far  as  sculpture  is  concerned,  the 
one  best  comparable  to  the  classic  period  of  Greek  art.  While 
sculpture  among  the  Maya  never  again  reached  so  high  a  degree  of 
perfection,  architecture  steadily  developed,  almost  to  the  last. 
Judging  from  the  dates  inscribed  upon  their  monuments,  all  the 
great  cities  of  the  south  flourished  during  this  period :  Palenque  and 
Yaxchilan  in  what  is  now  southern  Mexico;  Piedras  Negras,  Seibal, 
Tikal,  Naranjo,  and  Quirigua  in  the  present  Guatemala;  and  Copan 
in  the  present  Honduras.  AU  these  cities  rose  to  greatness  and  sank 
again  into  insignificance,  if  not  indeed  into  obhvion,  before  the  close 
of  this  Golden  Age. 

The  causes  which  led  to  the  decHne  of  civilization  in  the  south  are 
unknown.  It  has  been  conjectured  that  the  Maya  were  driven  from 
their  southern  homes  by  stronger  peoples  pushing  in  from  farther 
south  and  from  the  west,  or  again,  that  the  Maya  civihzation,  having 
run  its  natural  course,  collapsed  through  sheer  lack  of  inherent  power 
to  advance.  Which,  if  either,  of  these  hypotheses  be  true,  matters 
Httle,  since  in  any  event  one  all-important  fact  remains :  Just  after 
the  close  of  Cycle  9  of  Maya  chronology,  toward  the  end  of  the  sixth 
century,  there  is  a  sudden  and  final  cessation  of  dates  in  all  the 
southern  cities,  apparently  indicating  that  they  were  abandoned 
about  this  time. 

Still  another  condition  doubtless  hastened  the  general  decline  if 
indeed  it  did  no  more.  There  is  strong  documentary  evidence  ^  that 
about  the  middle  or  close  of  the  fifth  century  the  southern  part  of 
Yucatan  was  discovered  and  colonized.  In  the  century  following, 
the  southern  cities  one  by  one  sank  into  decay;  at  least  none  of  their 
monuments  bear  later  dates,  and  coincidently  Chichen  Itza,  the  first 
great  city  of  the  north,  was  founded  and  rose  to  prominence.  In 
the  absence  of  reUable  contemporaneous  records  it  is  impossible  to 
estabUsh  the  absolute  accxu"acy  of  any  theory  relating  to  times  so 

1  This  evidence  is  presented  by  The  Books  of  Chilan  Balam,  "which  were  copied  or  compiled  in  Yucatan 
by  natives  during  the  sixteenth,  seventeenth,  and  eighteenth  centuries,  from  much  older  manuscripts  now 
lost  or  destroyed.  They  are  written  in  the  Maya  language  in  Latin  characters,  and  treat,  in  part  at  least, 
of  the  history  of  the  country  before  the  Spanish  Conquest.  Each  town  seems  to  have  had  its  own  book  of 
Chaan  Balam,  distinguished  from  others  by  the  addition  of  the  name  of  the  place  where  it  was  written,  as: 
The  Book  of  Chilan  Balam  of  Mani,  The  Book  of  Chilan  Balam  of  Tizimin,  and  so  on.  Although  much  of  the 
material  presented  in  these  manuscripts  is  apparently  contradictory  and  obscure,  their  importance  as  original 
historical  sources  can  not  be  overestunated,  since  they  constitute  the  only  native  accounts  of  the  early 
history  of  the  Maya  race  which  have  survived  the  vandalism  of  the  Spanish  Conquerors.  Of  the  sixteen 
Books  of  Chilan  Balam  now  extant,  only  three,  those  of  the  towns  of  Mani,  Tizimin,  and  Chumayel, 
contain  historical  matter.  These  have  been  translated  into  English,  and  published  by  Dr.  D.  G,  Brinton 
[1882  b]  under  the  title  of  "  The  Maya  Chronicles."  This  translation  with  a  few  corrections  has  been 
freely  consulted  in  the  following  discussion."— Morley,  1910  b:  p.  193. 

Although  The  Books  of  Chilan  Balam  are  in  all  probability  authentic  sources  for  the  reconstruction  of 
Maya  history,  they  can  hardly  be  considered  contemporaneous  since,  as  above  explained,  they  emanate 
from  post-Conquest  times.  The  most  that  can  be  claimed  for  them  in  this  connection  is  that  the  docu- 
ments from  which  they  were  copied  were  probably  aboriginal,  and  contemporaneous,  or  approximately 
so,  with  the  later  periods  of  the  history  which  they  record. 


4 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


remote  as  those  here  under  consideration;  but  it  seems  not  improbable 
that  after  the  discovery  of  Yucatan  and  the  subsequent  opening  up 
of  that  vast  region,  the  southern  cities  commenced  to  dechne.  As 
the  new  country  waxed  the  old  waned,  so  that  by  the  end  of  the  sixth 
century  the  rise  of  the  one  and  the  fall  of  the  other  had  occurred. 

The  occupation  and  colonization  of  Yucatan  marked  the  dawn  of 
a  new  era  for  the  Maya  although  their  Renaissance  did  not  take  place 
at  once.  Under  pressure  of  the  new  environment,  at  best  a  parched 
and  waterless  land,  the  Maya  civihzation  doubtless  underwent  im- 
portant modification.^  The  period  of  colonization,  with  the  strenu- 
ous labor  by  which  it  was  marked,  was  not  conducive  to  progress  in 
the  arts.  At  first  the  struggle  for  bare  existence  must  have  absorbed 
in  a  large  measure  the  energies  of  all,  and  not  until  their  foothold  was 
secure  could  much  time  have  been  available  for  the  cultivation  of  the 
gentler  pm'suits.  Then,  too,  at  first  there  seems  to  have  been  a  feehng 
of  unrest  in  tlie  new  land,  a  shifting  of  homes  and  a  testing  of  locahties, 
all  of  which  retarded  the  development  of  architecture,  sculpture,  and 
other  arts.  Bakhalal  (see  pi.  1),  the  first  settlement  in  the  north,  was 
occupied  for  only  60  years.  Chichen  Itza,  the  next  location,  although 
occupied  for  more  than  a  century,  was  finally  abandoned  and  the  search 
for  a  new  home  resumed.  Moving  westward  from  Chichen  Itza,  Cha- 
kanputun  was  seized  and  occupied  at  the  beginning  of  the  eighth  cen- 
tiu*y.  Here  the  Maya  are  said  to  have  hved  for  260  years,  until  the 
destruction  of  Chakanputun  by  fire  about  960  A.  D.  again  set  them 
wandering.  By  this  time,  however,  some  four  centuries  had  elapsed 
since  the  first  colonization  of  the  country,  and  they  doubtless  felt 
themselves  fully  competent  to  cope  with  any  problems  arising  from 
their  environment.  Once  more  their  energies  had  begun  to  find  outlet 
in  artistic  expression.  The  Transitional  Period  was  at  an  end,  and 
The  Maya  Renaissance,  if  the  term  may  be  used,  was  fully  under  way. 

The  opening  of  the  eleventh  century  witnessed  important  and  far- 
reaching  political  changes  in  Yucatan.  After  the  destruction  of 
Chakanputun  the  honzon  of  Maya  activity  expanded.  Some  of  the 
fugitives  from  Chakanputun  reoccupied  Chichen  Itza  while  others 
estabfished  themselves  at  a  new  site  called  Mayapan.  About  tliis 
time  also  the  city  of  Uxmal  seems  to  have  been  founded.  In  the 
year  1000  these  three  cities— Cliichen  Itza,  Uxmal,  and  Mayapan — 
formed  a  confederacy,^  in  which  each  was  to  share  equally  in  the 
government  of  the  country.    Under  the  peaceful  conditions  which 

^As  will  appear  later,  on  the  calendric  side  the  old  system  of  counting  time  and  of  recording  events  gave 
place  to  a  more  abbreviated  though  less  accurate  chronology.  In  architecture  and  art  also  the  change  of 
environment  made  itself  felt,  and  in  other  lines  as  well  the  new  land  cast  a  strong  influence  over  Maya 
thought  and  achievement.  In  his  work  entitled  "A  Study  of  Maya  Art,  its  Subject  Matter  and  Historical 
Development"  (1913),  to  which  students  are  referred  for  further  information.  Dr.  H.  J.  Spinden  has 
treated  this  subject  extensively. 

2  The  confederation  of  these  three  Maya  cities  may  have  served  as  a  model  for  the  three  Nahua  cities, 
Tenochtitlan,  Tezcuco,  and  Tlacopan,  when  they  entered  into  a  similar  alliaace  some  foin:  centuries  later. 


MORLBY]      INTRODUCTION  TO  STIJDY  OF  MAYA  HIEROGLYPHS  5 


followed  the  formation  of  this  confederacy  for  the  next  200  years  the 
arts  blossomed  forth  anew. 

This  was  the  second  and  last  great  Maya  epoch.  It  was  their  Age 
of  Architecture  as  the  first  period  had  been  their  Age  of  Sculpture. 
As  a  separate  art  sculpture  languished;  but  as  an  adjunct,  an  embel- 
lishment to  architecture,  it  lived  again.  The  one  had  become  hand- 
maiden to  the  other.  Facades  were  treated  with  a  sculptural  deco- 
ration, which  for  intricacy  and  elaboration  has  rarely  been  equaled 
by  any  people  at  any  time;  and  yet  this  result  was  accomplished 
without  sacrifice  of  beauty  or  dignity.  During  this  period  probably 
there  arose  the  many  cities  which  to-day  are  crumbling  in  decay 
throughout  the  length  and  breadth  of  Yucatan,  their  very  names 
forgotten.  When  these  were  in  their  prime,  the  country  must  have 
been  one  great  beehive  of  activity,  for  only  a  large  population  could 
have  left  remains  so  extensive. 

This  era  of  universal  peace  was  abruptly  terminated  about  1200 
A.  D.  by  an  event  which  shook  the  body  poUtic  to  its  foundations 
and  disrupted  the  Triple  Alliance  under  whose  beneficent  rule  the 
land  had  grown  so  prosperous.  The  ruler  of  Chichen  Itza,  Chac  Xib 
Chac,  seems  to  have  plotted  against  his  colleague  of  Mayapan,  one 
Hunnac  Ceel,  and  in  the  disastrous  war  which  followed,  the  latter, 
with  the  aid  of  Nahua  allies,^  utterly  routed  his  opponent  and  drove 
him  from  his  city.  The  conquest  of  Chichen  Itza  seems  to  have  been 
followed  during  the  thirteenth  century  by  attempted  reprisals  on  the 
part  of  the  vanquished  Itza,  which  plunged  the  country  into  civil 
war;  and  this  struggle  in  turn  paved  the  way  for  the  final  ecUpse  of 
Maya  supremacy  in  the  fifteenth  century. 

After  the  dissolution  of  the  Triple  Alliance  a  readjustment  of 
power  became  necessary.  It  was  only  natural  that  the  victors  in  the 
late  war  should  assume  the  chief  direction  of  affairs,  and  there  is 
strong  evidence  that  Mayapan  became  the  most  important  city  in 
the  land.  It  is  not  improbable  also  that  as  a  result  of  this  war 
Chichen  Itza  was  turned  over  to  Hunnac  CeeFs  Nahua  allies,  perhaps 
in  recognition  of  their  timely  assistance,  or  as  their  share  in  the  spoils 
of  war.  It  is  certain  that  sometime  during  its  history  Chichen  Itza 
came  under  a  strong  Nahua  influence.  One  group  of  buildings  in 
particular  ^  shows  in  its  architecture  and  bas-reliefs  that  it  was 
undoubtedly  inspired  by  Nahua  rather  than  by  Maya  ideals. 

According  to  Spanish  historians,  the  fourteenth  century  was  char- 
acterized by  increasing  arrogance  and  oppression  on  the  part  of  the 
rulers  of  Mayapan,  who  found  it  necessary  to  surround  themselves 
with  Nahua  alhes  in  order  to  keep  the  rising  discontent  of  their  sub- 


1  By  Nahua  is  here  meant  the  peoples  who  inhabited  the  valley  of  Mexico  and  adjacent  territory  at  this 
time. 

2  The  Ball  Court,  a  characteristically  Nahua  development. 


6 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


jects  in  check.^  This  unrest  finally  reached  its  culmination  about 
the  middle  of  the  fifteenth  century,  when  the  Maya  nobility,  unable 
longer  to  endure  such  tyranny,  banded  themselves  together  under 
the  leadership  of  the  lord  of  Uxmal,  sacked  Mayapan,  and  slew  its 
ruler. 

All  authorities,  native  as  well  as  Spanish,  agree  that  the  destruc- 
tion of  Mayapfin  marked  the  end  of  strongly  centralized  government 
in  Yucatan.  Indeed  there  can  be  but  little  doubt  that  this  event 
also  sounded  the  death  knell  of  Maya  civilization.  As  one  of  the 
native  chronicles  tersely  puts  it,  ^'The  chiefs  of  the  country  lost  their 
power."  With  the  destruction  of  Mayapan  the  country  split  into  a 
number  of  warring  factions,  each  bent  on  the  downfall  of  the  others. 
Ancient  jealousies  and  feuds,  no  longer  held  in  leash  by  the  restrain- 
ing hand  of  Mayapan,  doubtless  revived,  and  soon  the  land  was  rent 
with  strife.  Presently  to  the  horrors  of  civil  war  were  added  those 
of  famine  and  pestilence,  each  of  which  visited  the  peninsula  in  turn, 
carrying  off  great  numbers  of  people. 

These  several  calamities,  however,  were  but  harbingers  of  worse 
soon  to  come.  In  1517  Francisco  de  Cordoba  landed  the  first  Spanish 
expedition  ^  on  the  shores  of  Yucatan.  The  natives  were  so  hostile, 
however,  that  he  returned  to  Cuba,  having  accomplished  little  more 
than  the  discovery  of  the  country.  In  the  following  year  Juan  de 
Grijalva  descended  on  the  peninsula,  but  he,  too,  met  with  so  deter- 
mined a  resistance  that  he  sailed  away,  having  gained  little  more 
than  hard  knocks  for  his  pains.  In  the  followiQg  year  (1519)  Her- 
nando Cortez  landed  on  the  northeast  coast  but  reembarked  in  a  few 
days  for  Mexico,  again  leaving  the  courageous  natives  to  themselves. 
Seven  years  later,  however,  in  1526,  Francisco  Montejo,  having  been 
granted  the  title  of  Adelantado  of  Yucatan,  set  about  the  conquest 
of  the  country  in  earnest.  Having  obtained  the  necessary  '^sinews 
of  war"  through  his  marriage  to  a  wealthy  widow  of  Seville,  he  sailed 
with  3  ships  and  500  men  for  Yucatan.  He  first  landed  on  the 
island  of  Cozumel,  off  the  northeast  coast,  but  soon  proceeded  to 
the  mainland  and  took  formal  possession  of  the  country  in  the 
name  of  the  King  of  Spain.    This  empty  ceremony  soon  proved  to  be 

1  One  authority  (Landa,  1864:  p.  48)  says  in  this  connection:  "The  governor, Cocom— the  ruler  of  Maya- 
pan—began  to  covet  riches;  and  for  this  purpose  he  treated  with  the  people  of  the  garrison,  which  the 
kings  of  Mexico  nad  in  Tabasco  and  Xicalango,  that  he  should  deliver  his  city  [i.  e.  Mayapan]  to  them; 
and  thus  he  brought  the  Mexican  people  to  Mayapan  and  he  oppressed  the  poor  and  made  many  slaves, 
and  the  lords  would  have  killed  him  if  they  had  not  been  afraid  of  the  Mexicans." 

2  The  first  appearance  of  the  Spaniards  in  Yucatan  was  six  years  earlier  (in  1511),  when  the  caravel  of 
Valdivia,  returning  from  the  Isthmus  of  Darien  to  Hispaniola,  foundered  near  Jamaica.  About  10  sur- 
vivors in  an  open  boat  were  driven  upon  the  coast  of  Yucatan  near  the  Island  of  Cozumel.  Here  they 
were  made  prisoners  by  the  Maya  and  five,  including  Valdivia  himself,  were  sacrificed.  The  remainder 
escaped  only  to  die  of  starvation  and  hardship,  with  the  exception  of  two,  Geronimo  de  Aguilar  and 
Gonzalo  Guerrero.  Both  of  these  men  had  risen  to  considerable  prominence  in  the  country  by  the  time 
Cortez  arrived  eight  years  later.  Guerrero  had  married  a  chief's  daughter  and  had  himself  become  a  chief. 
Later  Aguilar  became  an  interpreter  for  Cortez.  This  handful  of  Spaniards  can  hardly  be  called  an  expe- 
dition, however. 


MOELET]      INTRODUCTION  TO  STUDY  OP  MAYA  HIEEOGLYPHS 


1 


but  the  prelude  to  a  sanguinary  struggle,  which  broke  out  ahnost 
immediately  and  continued  with  extraordinary  ferocity  for  many 
years,  the  Maya  fighting  desperately  m  defense  of  their  homes. 
Indeed,  it  was  not  until  14  years  later,  on  June  11,  1541  (old  style), 
that,  the  Spaniards  having  defeated  a  coalition  of  Maya  chieftains 
near  the  city  of  Ichcanzihoo,  the  conquest  was  finally  brought  to  a 
close  and  the  pacification  of  the  country  accomplished.  With  this 
event  ends  the  independent  history  of  the  Maya. 

Manners  and  Customs 

AccordiQg  to  Bishop  Landa,^  who  wrote  his  remarkable  history  of 
Yucatan  in  1565,  the  Maya  of  that  day  were  a  tall  race,  active  and 
strong.  In  childhood  the  forehead  was  artificially  flattened  and  the 
ears  and  nose  were  pierced  for  the  insertion  of  earrings  and  nose-orna- 
ments, of  which  the  people  were  very  fond.  Squint-eye  was  consid- 
ered a  mark  of  beauty,  and  mothers  strove  to  disfigure  their  children 
in  this  way  by  suspending  pellets  of  wax  between  their  eyes  in  order 
to  make  them  squint,  thus  securing  the  desired  effect.  The  faces  of 
the  younger  boys  were  scalded  by  the  application  of  hot  cloths,  to 
prevent  the  growth  of  the  beard,  which  was  not  popular.  Both  men 
and  women  wore  their  hair  long.  The  former  had  a  large  spot  burned 
on  the  back  of  the  head,  where  the  hair  always  remained  short.  With 
the  exception  of  a  small  queue,  which  hung  down  behind,  the  hair 
was  gathered  around  the  head  in  a  braid.  The  women  wore  a  more 
beautiful  coiffure  divided  into  two  braids.  The  faces  of  both  sexes 
were  much  disfigured  as  a  result  of  their  rehgious  beliefs,  which  led 
to  the  practice  of  scarification.  Tattooing  also  was  common  to  both 
sexes,  and  there  were  persons  ia  ahnost  every  community  who  were 
especially  proficient  in  this  art.  Both  men  and  women  painted 
themselves'  red,  the  former  decorating  their  entire  bodies,  and  the 
latter  all  except  their  faces,  which  modesty  decreed  should  be  left 
unpainted.  The  women  also  anointed  themselves  very  freely  with 
fragrant  gums  and  perfumes.  They  filed  their  teeth  to  sharp  points, 
a  practice  which  was  thought  to  enhance  their  beauty. 

The  clothing  of  the  men  was  simple.  They  wore  a  breechclout 
wrapped  several  times  around  the  loins  and  tied  in  such  a  way  that 
one  end  fell  in  front  between  the  legs  and  the  other  in  the  correspond- 

1  Diego  de  Landa,  second  bishop  of  Merida,  whose  remarkable  book  entitled  "Relacion  de  las  Cosas  de 
Yucatan"  is  the  chief  authority  for  the  facts  presented  in  the  following  discussion  of  the  manners  and 
customs  of  the  Maya,  was  born  in  Cifuentes  de  I'Alcarria,  Spain,  in  1524.  At  the  age  of  17 he  joined  the 
Franciscan  order.  He  came  to  Yucatan  during  the  decade  following  the  close  of  the  Conquest,  in  1549, 
where  he  was  one  of  the  most  zealous  of  the  early  missionaries.  In  1573  he  was  appointed  bishop  of  Merida, 
which  position  he  held  until  his  death  in  1579.  His  priceless  Relacion,  written  about  1565,  was  not  printed 
until  three  centuries  later,  when  it  was  discovered  by  the  indefatigable  Abb6  Brasseur  de  Bourbourg  in 
the  library  of  the  Royal  Academy  of  History  at  Madrid,  and  published  by  him  in  1864.  The  Relacion 
is  the  standard  authority  for  the  customs  prevalent  in  Yucatan  at  the  time  of  the  Conquest,  and  is  an 
invaluable  aid  to  the  student  of  Maya  archeology.  What  little  we  know  of  the  Maya  calendar  has  been 
derived  du-ectly  from  the  pages  of  this  book,  or  by  developing  the  material  therein  presented. 


8 


BUEEAU  OF  AMERICAN  ETHNOLOGY 


[bull,  57 


ing  position  behind.  These  breechclouts  were  carefully  embroidered 
by  the  women  and  decorated  with  featherwork.  A  large  square  cape 
hung  from  the  shoulders,  and  sandals  of  hemp  or  leather  completed 
the  costume.  For  persons  of  high  rank  the  apparel  was  much  more 
elaborate,  the  humble  breechclout  and  cape  of  the  laboring  man 
giving  place  to  panaches  of  gorgeously  colored  feathers  hanging  from 
wooden  helmets,  rich  mantles  of  tiger  skins,  and  finely  wrought  orna- 
ments of  gold  and  jade. 

The  women  sometimes  wore  a  simple  petticoat,  and  a  cloth  covering 
the  breasts  and  passing  under  the  arms.  More  often  their  costume 
consisted  of  a  single  loose  sacklike  garment  called  the  Jiipil,  which 
reached  to  v  the  feet  and  had  slits  for  the  arms.  This  garment,  with 
the  addition  of  a  cloth  or  scarf  wrapped  around  the  shoulders,  con- 
stituted the  women's  clothing  a  thousand  years  ago,  just  as  it  does 
to-day. 

In  ancient  times  the  women  were  very  chaste  and  modest.  When 
they  passed  men  on  the  road  they  stepped  to  one  side,  turning  their 
backs  and  hiding  their  faces.  The  age  of  marriage  was  about  20, 
although  children  were  frequently  affianced  when  very  young.  When 
boys  arrived  at  a  marriageable  age  their  fathers  consulted  the  pro- 
fessional matchmakers  of  the  commxmity,  to  whom  arrangements  for 
marriage  were  ordinarily  intrusted,  it  being  considered  vulgar  for 
parents  or  their  sons  to  take  an  active  part  in  arranging  these  affairs. 
Having  sought  out  the  girl's  parents,  the  matchmaker  arranged  with 
them  the  matter  of  the  dowry,  which  the  young  man's  father  paid, . 
his  wife  at  the  same  time  giving  the  necessary  clothing  for  her  son 
and  prospective  daughter-in-law.  On  the  day  of  the  wedding  the 
relatives  and  guests  assembled  at  the  house  of  the  young  man's 
parents,  where  a  great  feast  had  been  prepared.  Having  satisfied 
himself  that  the  young  couple  had  sufficiently  considered  the  grave 
step  they  were  about  to  take,  the  priest  gave  the  bride  to  her  hus- 
band. The  ceremony  closed  with  a  feast  in  which  all  participated. 
Immediately  after  the  wedding  the  young  husband  went  to  the  home 
of  his  wife's  parents,  where  he  was  obliged  to  work  five  or  six  years 
for  his  board.  If  he  refused  to  comply  with  this  custom  he  was 
driven  from  the  house,  and  the  marriage  presumably  was  annulled. 
This  step  seems  rarely  to  have  been  necessary,  however,  and  the 
mother-in-law  on  her  part  saw  to  it  that  her  daughter  fed  the  young 
husband  regularly,  a  practice  which  betokened  their  recognition  of 
the  marriage  rite. 

Widowers  and  widows  married  without  ceremony,  it  being  consid- 
ered sufficient  for  a  widower  to  call  on  his  prospective  wife  and  eat  in 
her  house.  Marriage  between  people  of  the  same  name  was  con- 
sidered an  evil  practice,  possibly  in  deference  to  some  former  exogamic 
law.    It  was  thought  improper  to  marry  a  mother-in-law  or  an  aunt 


MORLEY]      INTKODUCTIOK  TO  STUDY  OF  MAYA  HIEROGLYPHS  9 

by  marriage,  or  a  sister-in-law;  otherwise  a  man  could  marry  whom 
he  would,  even  his  first  cousin. 

The  Maya  were  of  a  very  jealous  nature  and  divorces  were  frequent. 
These  were  effected  merely  by  the  desertion  of  the  husband  or  wife, 
as  the  case  might  be.  The  parents  tried  to  bring  the  couple  together 
and  effect  a  reconciliation,  but  if  their  efforts  proved  unsuccessful 
both  parties  were  at  liberty  to  remarry.  If  there  were  young  children 
the  mother  kept  them;  if  the  children  were  of  age  the  sons  followed 
the  father,  the  daughters  remaining  with  their  mother.  Although 
divorce  was  of  common  occurrence,  it  was  condemned  by  the  more 
respectable  members  of  the  community.  It  is  interesting  to  note 
that  polygamy  was  unknown  among  the  Maya. 

Agriculture  was  the  chief  pursuit,  corn  and  other  grains  being 
extensively  cultivated,  and  stored  against  time  of  need  in  well- 
appointed  granaries.  Labor  was  largely  communal;  all  hands  joined 
to  do  one  another's  work.  Bands  of  twenty  or  more  each,  passing 
from  field  to  field  throughout  the  community,  quickly  finished  sowing 
or  harvesting.  This  communal  idea  was  carried  to  the  chase,  fifty  or 
more  men  frequently  going  out  together  to  hunt.  At  the  conclusion 
of  these  expeditions  the  meat  was  roasted  and  then  carried  back  to 
town.  First,  the  lord  of  the  district  was  given  his  share,  after  which 
the  remainder  was  distributed  among  the  hunters  and  their  friends. 
Communal  fishing  parties  are  also  mentioned. 

Another  occupation  in  high  favor  was  that  of  trade  or  commerce. 
Salt,  cloth,  and  slaves  were  the  chief  articles  of  barter;  these  were 
carried  as  far  as  Tabasco.  Cocoa,  stone  counters,  and  highly  prized 
red  shells  of  a  peculiar  kind  were  the  media  of  exchange.  These  were 
accepted  in  return  for  all  the  products  of  the  country,  even  includ- 
ing the  finely  worked  stones,  jades  possibly,  with  which  the  chiefs 
adorned  themselves  at  their  fetes.  Credit  was  asked  and  given,  all 
debts  were  honestly  paid,  and  no  usury  was  exacted. 

The  sense  of  justice  among  the  Maya  was  highly  developed.  If  a 
man  committed  an  offense  against  one  of  another  village,  the  former's 
lord  caused  satisfaction  to  be  rendered,  otherwise  the  communities 
would  come  to  blows.  Troubles  between  men  of  the  same  village 
were  taken  to  a  judge,  who  having  heard  both  sides,  fixed  appropriate 
damages.  If  the  malefactor  could  not  pay  these,  the  obligation 
extended  to  his  wife  and  relatives.  Crimes  which  could  be  satisfied 
by  the  payment  of  an  indemnity  were  accidental  killings,  quarrels 
between  man  and  wife,  and  the  accidental  destruction  of  property  by 
fire.  Malicious  mischief  could  be  atoned  for  only  by  blows  and  the 
shedding  of  blood.  The  punishment  of  murder  was  left  in  the  hands 
of  the  deceased's  relatives,  who  were  at  liberty  to  exact  an  indemnity 
or  the  murderer's  life  as  they  pleased.  The  thief  was  obliged  to  make 
good  whatever  he  had  stole q,  no  matter  how  little;  in  event  of  failure 
to  do  so  he  was  reduced  to  slavery.    Adultery  was  punishable  by 


10 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


death.  The  adulterer  was  led  mto  the  courtyard  of  the  chief's  house, 
where  all  had  assembled,  and  after  being  tied  to  a  stake,  was  turned 
over  to  the  mercies  of  the  outraged  husband,  who  either  pardoned 
him  or  crushed  his  head  with  a  heavy  rock.  As  for  the  guilty  woman, 
her  infamy  was  deemed  sufficient  punishment  for  her,  though  usually 
her  husband  abandoned  her. 

The  Maya  were  a  very  hospitable  people,  always  offering  food  and 
drink  to  the  stranger  within  their  gates,  and  sharing  with  him  to  the 
last  crumb.  They  were  much  given  to  conviviality,  particularly  the 
lords,  who  frequently  entertained  one  another  with  elaborate  feasts, 
accompanied  by  music  and  dancing,  expending  at  tunes  on  a  single 
occasion  the  proceeds  of  many  days'  accumulation.  They  usually 
sat  down  to  eat  by  twos  or  fours.  The  meal,  which  consisted  of 
vegetable  stews,  roast  meats,  com  cakes,  and  cocoa  (to  mention  only 
a  few  of  the  viands)  was  spread  upon  mats  laid  on  the  ground.  After 
the  repast  was  finished  beautiful  young  girls  acting  as  cupbearers 
passed  among  the  guests,  plying  them  industriously  with  wine  until 
all  were  drunk.  Before  departing  each  guest  was  presented  with  a 
handsome  vase  and  pedestal,  with  a  cloth  cover  therefor.  At  these 
orgies  drinking  was  frequently  carried  to  such  excess  that  the  wives 
of  the  guests  were  obliged  to  come  for  their  besotted  husbands  and 
drag  them  home.  Each  of  the  guests  at  such  a  banquet  was  required 
to  give  one  in  return,  and  not  even  death  could  stay  the  payment  of 
a  debt  of  this  kind,  since  the  obligation  descended  to  the  recipient's 
heirs.  The  poor  entertained  less  lavishly,  as  became  their  means. 
Guests  at  the  humbler  feasts,  moreover,  were  not  obliged  to  return 
them  in  kind. 

The  chief  amusements  of  the  Maya  were  comedies  and  dances,  in 
both  of  which  they  exhibited  much  skill  and  ingenuity.  There  was 
a  variety  of  musical  instruments — drums  of  several  kinds,  rattles, 
reed  flutes,  wooden  horns,  and  bone  whistles.  Their  music  is 
described  as  having  been  sad,  owing  perhaps  to  the  melancholy  sound 
of  the  instruments  which  produced  it. 

The  frequent  wars  which  darken  the  final  pages  of  Maya  history 
doubtless  developed  the  military  organization  to  a  high  degree  of 
efficiency.  At  the  head  of  the  army  stood  two  generals,  one  hereditary 
and  the  other  elective  {nacon)j  the  latter  serving  for  three  years.  In 
each  village  throughout  the  country  certain  men  (holcanes)  were 
chosen  to  act  as  soldiers;  these  constituted  a  kind  of  a  standing  army, 
thoroughly  trained  in  the  art  of  war.  They  were  supported  by  the 
community,  and  in  times  of  peace  caused  much  disturbance,  con- 
tinuing the  tumult  of  war  after  war  had  ceased.  In  times  of  great 
stress  when  it  became  necessary  to  call  on  all  able-bodied  men  for 
military  service,  the  holcanes  mustered  all  those  available  in  their 
respective  districts  and  trained  them  in  the  use  of  arms.  There  were 
but  few  weapons:  Wooden  bows  strung  with  hemp  cords,  and  arrows 


MORLEY]      INTBODUCTIOK  TO  STUDY  OF  MAYA  HIEROGLYPHS 


11 


tipped  with  obsidian  or  bone;  long  lances  with  sharp  flint  points; 
and  metal  (probably  copper)  axes,  provided  with  wooden  handles. 
The  defensive  armor  consisted  of  round  wicker  shields  strengthened 
with  deer  hide,  and  quilted  cotton  coats,  which  were  said  to  have 
extraordinary  resisting  power  against  the  native  weapons.  The 
highest  chiefs  wore  wooden  helmets  decorated  with  brilliant  plumes, 
and  cloaks  of  ^Higer'^  (jaguar)  skin,  thrown  over  their  shoulders. 

With  a  great  banner  at  their  head  the  troops  silently  stole  out  of 
the  city,  and  moved  against  the  enemy,  hoping  thus  to  surprise  them. 
When  the  enemies'  position  had  been  ascertained,  they  fell  on  them 
suddenly  with  extraordinary  ferocity,  uttering  loud  cries.  Barricades 
of  trees,  brush,  and  stone  were  used  in  defense,  behind  which  archers 
stood,  who  endeavored  to  repulse  the  attack.  After  a  battle  the 
victors  mutilated  the  bodies  of  the  slain,  cutting  out  the  jawbones 
and  cleaning  them  of  flesh.  These  were  worn  as  bracelets  after  the 
flesh  had  been  removed.  At  the  conclusion  of  their  wars  the  spoils 
were  offered  in  sacrifice.  If  by  chance  some  leader  or  chief  had  been 
captured,  he  was  sacrificed  as  an  offering  particularly  acceptable  to 
the  gods.  Other  prisoners  became  the  slaves  of  those  who  had 
captured  them. 

The  Maya  entertained  an  excessive  and  constant  fear  of  death, 
many  of  their  religious  practices  having  no  other  end  in  view  than 
that  of  warding  off  the  dread  visitor.  After  death  there  followed  a 
prolonged  period  of  sadness  in  the  bereaved  family,  the  days  being 
given  over  to  fasting,  and  the  more  restrained  indulgence  in  grief, 
and  the  nights  to  dolorous  cries  and  lamentations,  most  pitiful  to 
hear.  Among  the  common  people  the  dead  were  wrapped  in  shrouds; 
their  mouths  were  filled  with  ground  corn  and  bits  of  worked  stone 
so  that  they  should  not  lack  for  food  and  money  in  the  life  to  come. 
The  Maya  buried  their  dead  inside  the  houses  ^  or  behind  them, 
putting  into  the  tomb  idols,  and  objects  indicating  the  profession  of 
the  deceased — if  a  priest,  some  of  his  sacred  books;  if  a  seer,  some 
of  his  divinatory  paraphernalia.  A  house  was  commonly  abandoned 
after  a  death  therein,  unless  enough  remained  in  the  household  to 
dispel  the  fear  which  always  followed  such  an  occurrence. 

In  the  higher  walks  of  life  the  mortuary  customs  were  more  elabo- 
rate. The  bodies  of  chiefs  and  others  of  high  estate  were  burned 
and  their  ashes  placed  in  large  pottery  vessels.  These  were  buried 
in  .the  ground  and  temples  erected  over  them.^    When  the  deceased 

1  The  excavations  of  Mr.  E.  H.  Thompson  at  Labna,  Yucatan,  and  of  Dr.  Merwin  at  Holmul,  Guatemala, 
have  confirmed  Bishop  Landa's  statement  concerntiig  the  disposal  of  the  dead.  At  Lahna  bodies  were 
found  buried  beneath  the  floors  of  the  buildiags,  and  at  Holmul  not  only  beneath  the  floors  but  also  lying 
on  them. 

2  Examples  of  this  type  of  burial  have  been  foimd  at  Chichen  Itza  and  Mayapan  in  Yucatan.  At  the 
former  site  Mr.  E.  H.  Thompson  found  in  the  center  of  a  large  pyramid  a  stone-lined  shaft  running  from 
the  summit  into  the  ground.  This  was  filled  with  burials  and  fvmeral  objects--pearls,  coral,  and  jade, 
which  from  their  precious  nature  indicated  the  remains  of  important  personages.  At  Mayapan,  burials 
were  fovmd  in  a  shaft  of  similar  construction  and  location  in  one  of  the  pyramids. 


12 


BUREAtJ  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


was  of  very  high  rank  the  pottery  sarcophagus  took  the  form  of 
a  human  statue.  A  variant  of  the  above  procedure  was  to  burn 
only  a  part  of  the  body,  inclosing  the  ashes  in  the  hollow  head  of  a 
wooden  statue,  and  sealing  them  in  with  a  piece  of  skin  taken  from 
the  back  of  the  dead  man's  skull.  The  rest  of  the  body  was  buried. 
Such  statues  were  jealously  preserved  among  the  figures  of  the  gods, 
being  held  in  deep  veneration. 

The  lords  of  Mayapan  had  still  another  mortuary  practice.  After 
death  the  head  was  severed  from  the  body  and  cooked  in  order  to 
remove  all  flesh.  It  was  then  sawed  in  half  from  side  to  side,  care 
being  taken  to  preserve  the  jaw,  nose,  eyes,  and  forehead  in  one  piece. 
Upon  this  as  a  form  the  features  of  the  dead  man  were  filled  in  with 
a  kind  of  a  gum.  Such  was  their  extraordinary  skill  in  this  peculiar 
work  that  the  finished  mask  is  said  to  have  appeared  exactly  like  the 
countenance  in  life.  The  carefully  prepared  faces,  together  with  the 
statues  containing  the  ashes  of  the  dead,  were  deposited  with  their 
idols.  Every  feast  day  meats  were  set  before  them  so  they  should 
lack  for  nothing  in  that  other  world  whither  they  had  gone. 

Very  little  is  known  about  the  governmental  organization  of  the 
southern  Maya,  and  it  seems  best,  therefore,  first  to  examine  conditions 
in  the  north,  concerning  which  the  early  authorities,  native  as  well 
as  Spanish,  have  much  to  say.  The  northern  Maya  lived  in  settle- 
ments, some  of  very  considerable  extent,  under  the  rule  of  hereditary 
chiefs  called  halach  uinicil,  or  '^real  men,"  who  were,  in  fact  as  well 
as  name,  the  actual  rulers  of  the  country.  The  settlements  tribu- 
tary to  each  Jialach  uinic  were  doubtless  connected  by  tribal  ties, 
based  on  real  or  fancied  blood  relationship. 

During  the  period  of  the  Triple  Alliance  (1000-1200  A.  D.)  there 
were  probably  only  three  of  these  embryonic  nations:  Chichen  Itza, 
Uxmal,  and  Mayapan,  among  which  the  country  seems  to  have  been 
apportioned.  After  the  conquest  of  Chichen  Itza,  however,  the 
halach  uinic  of  Mayapan  probably  attempted  to  establish  a  more 
autocratic  form  of  government,  arrogating  to  himself  still  greater 
power.  The  Spanish  authorities  relate  that  the  chiefs  of  the  country 
assembled  at  Mayapan,  acknowledged  the  ruler  of  that  city  as  their 
overlord,  and  finally  agreed  to  live  there,  each  binding  himself  at  the 
same  time  to  conduct  the  affairs  of  his  own  domain  through  a  deputy. 

This  attempt  to  unite  the  country  under  one  head  and  bring  about 
a  further  centralization  of  power  ultimately  failed,  as  has  been  seen, 
through  the  tyranny  of  the  Cocom  family,  in  wMch  the  ofiice  of  halach 
uinic  of  Mayapan  was  vested.  This  tyranny  led  to  the  overthrow 
of  the  Cocoms  and  the  destruction  of  centralized  government,  so  that 
when  the  Spaniards  arrived  they  found  a  number  of  petty  chieftains, 
acknowledging  no  overlord,  and  the  country  in  chaos. 

The  powers  of  the  halach  uinic  are  not  clearly  understood.  He  seems 
to  have  stood  at  the  apex  of  the  governmental  organization,  and  doubt- 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


13 


less  his  will  prevailed  just  so  far  as  he  had  sufficient  strength  to  enforce 
it.  The  hatahs,  or  underchiefs,  were  obliged  to  visit  him  and  render  him 
their  homage.  They  also  accompanied  him  in  his  tours  about  the 
country,  which  always  gave  rise  to  feasting  back  and  forth.  Finally 
they  advised  him  on  all  important  matters.  The  office  would  seem 
to  have  been  no  stronger  in  any  case  than  its  incumbent,  since  we 
hear  of  the  halach  uinic  of  Mayapan  being  obliged  to  surround  himself 
with  foreign  troops  in  order  to  hold  his  people  in  check. 

Each  batab  governed  the  territory  of  which  he  was  the  hereditary 
ruler,  instructing  his  heir  in  the  duties  of  the  position,  and  counseling 
that  he  treat  the  poor  with  benevolence  and  maintain  peace  and 
encourage  industry,  so  that  all  might  live  in  plenty.  He  settled  all 
lawsuits,  and  through  trusted  lieutenants  ordered  and  adjusted  the 
various  affairs  of  his  domain.  When  he  went  abroad  from  his  city 
or  even  from  his  house  a  great  crowd  accompanied  him.  He  often  vis- 
ited his  underchiefs,  holding  court  in  their  houses,  and  meeting  at  night 
in  council  to  discuss  matters  touching  the  common  good.  The  batabs 
frequently  entertained  one  another  with  dancing,  hunting,  and  feast- 
ing. The  people  as  a  community  tilled  the  batab's  fields,  reaped  his 
corn,  and  supplied  his  wants  in  general.  The  underchiefs  were  simi- 
larly provided  for,  each  according  to  his  rank  and  needs. 

The  aJikulelj  the  next  highest  official  in  each  district,  acted  as  the 
batab's  deputy  or  representative;  he  carried  a  short  thick  baton  in 
token  of  his  office.  He  had  charge  of  the  localities  subject  to  his 
master's  rule  as  well  as  of  the  officers  immediately  over  them.  He 
kept  these  assistants  informed  as  to  what  was  needed  in  the  batab's 
house,  as  birds,  game,  fish,  corn,  honey,  salt,  and  cloth,  which  they 
supplied  when  called  on.  The  ahkulel  was,  in  short,  a  chief  steward, 
and  his  house  was  the  batab's  business  office. 

Another  important  position  was  that  of  the  nacon,  or  war-chief. 
In  times  of  war  this  functionary  was  second  only  to  the  hereditary 
chief,  or  batab,  and  was  greatly  venerated  by  all.  His  office  was 
elective,  the  term  being  three  years,  during  which  he  was  obliged  to 
refrain  from  intercourse  with  women,  and  to  hold  himself  aloof  from  all. 

An  important  civil  position  was  that  held  by  the  aJiholpop,  in 
whose  keeping  was  the  tunkul,  or  wooden  drum,  used  in  summoning 
people  to  the  dances  and  public  meetings,  or  as  a  tocsin  in  case  of  war. 
He  had  charge  also  of  the  "town  hall"  in  which  all  public  business 
was  transacted. 

The  question  of  succession  is  important.  Bishop  Landa  distinctly 
states  in  one  passage  "That  when  the  lord  died,  although  his  oldest 
son  succeeded  him,  the  others  were  always  loved  and  served  and  even 
regarded  as  lords."  This  would  seem  to  indicate  definitely  that 
descent  was  by  primogeniture.  However,  another  passage  suggests 
that  the  oldest  son  did  not  always  succeed  his  father:  "The  lords 
were  the  governors  and  confirmed  their  sons  in  their  offices  if  they 


14 


BUREAU  or  AMERICAN  ETHNOLOGY 


[BULL,  57 


[the  sons]  were  acceptable."  This  suggests  the  possibihty,  at  least, 
that  primogeniture  could  sometimes  be  set  aside,  particularly  when 
the  first-born  lacked  the  necessary  qualifications  for  leadership.  In 
a  somewhat  drawn-out  statement  the  same  authority  discusses  the 
the  question  of  "princely  succession"  among  the  Maya: 

If  the  children  were  too  young  to  be  intrusted  with  the  management  of  their  own 
affairs,  these  were  turned  over  to  a  guardian ,  the  nearest  relation .  He  gave  the  children 
to  their  mothers  to  bring  up,  because  according  to  their  usage  the  mother  has  no  power 
of  her  own.  When  the  guardian  was  the  brother  of  the  deceased  [the  children's 
paternal  uncle]  they  take  the  children  from  their  mother.  These  guardians  give  what 
was  intrusted  to  them  to  the  heirs  when  they  come  of  age,  and  not  to  do  so  was  considered 
a  great  dishonesty  and  was  the  cause  of  much  contention.  ...  If  when  the  lord  died 
there  were  no  sons  [ready,  i.  e.,  of  age]  to  rule  and  he  had  brothers,  the  oldest  or  most 
capable  of  his  brothers  ruled,  and  they  [the  guardians]  showed  the  heir  the  customs 
and  fetes  of  his  people  until  he  should  be  a  man,  and  these  brothers,  although  the  heir 
were  [ready]  to  rule,  commanded  all  their  lives,  and,  if  there  were  no  brothers  the 
priests  and  principal  people  selected  a  man  suitable  for  the  position.^ 

The  foregoing  would  seem  to  imply  that  the  rulers  were  succeeded 
by  their  eldest  sons  if  the  latter  were  of  age  and  otherwise  generally 
acceptable;  and  that,  if  they  were  minors  when  their  fathers  died, 
their  paternal  uncles,  if  any,  or  otherwise  some  capable  man  selected 
by  the  priests,  took  the  reins  of  government,  instructing  the  heir  in 
the  duties  of  the  position  which  he  was  to  occupy  some  day;  and 
finally  that  the  regent  did  not  lay  down  his  authority  until  death, 
even  tliou^gh  the  heir  had  previously  attained  his  majority.  This 
custom  is  so  unusual  that  its  existence  may  well  be  doubted,  and  it 
is  not  at  all  improbable  that  Bishop  Landa's  statement  to  the  con- 
trary may  have  arisen  from  some  misapprehension.  Primogeniture 
was  not  confined  to  the  executive  succession  alone,  since  Bishop  Landa 
states  further  that  the  high  priest  Ahau  can  mai  was  succeeded  in 
his  dignity  by  his  sons,  or  those  next  of  kin. 

Nepotism  doubtless  prevailed  extensively,  all  the  higher  offices  of 
the  priesthood  as  well  as  the  executive  offices  being  hereditary,  and 
in  all  probabihty  filled  with  members  of  the  halach  uinic's  family.. 

The  priests  instructed  the  younger  sons  of  the  ruling  family  as  well 
as  their  own,  in  the  priestly  duties  and  learning;  in  the  computation  of 
years,  months,  and  days;  in  unlucky  times;  in  fetes  and  ceremonies; 
in  the  administration  of  the  sacraments;  in  the  practices  of  prophecy 
and  divination;  in  treating  the  sick;  in  their  ancient  history;  and 
finally  in  the  art  of  reading  and  writing  their  hieroglyphics,  which  was 
taught  only  to  those  of  high  degree.  Genealogies  were  carefully 
preserved,  the  term  meaning  ''of  noble  birth"  being  ah  Icaha,  "he  who 
has  a  name. ' '  The  elaborate  attention  given  to  the  subject  of  lineage, 
and  the  exclusive  right  of  the  all  Icaha  to  the  benefits  of  education, 
show  that  in  the  northern  part  of  the  Maya  territory  at  least  govern- 


1  Landa,  1864:  p.  137. 


MORDBY]      INTEODUCTION"  TO  SOTUDY  OF  MAYA  HIEROGLYPHS 


15 


ment  rested  on  the  principle  of  hereditary  succession.  The  accounts 
of  native  as  well  as  of  Spanish  writers  leave  the  impression  that  a 
system  not  unlike  a  modified  form  of  feudalism  prevailed. 

In  attempting  to  gain  an  approximate  understanding  of  the  form 
of  government  which  existed  in  the  southern  part  of  the  Maya  terri- 
ritory  it  is  necessary  in  the  absence  of  all  documentary  information 
to  interpret  the  southern  chronology,  architecture,  and  sculpture — 
practically  all  that  remains  of  the  older  culture — in  the  light  of  the 
known  conditions  in  the  north.  The  chronology  of  the  several 
southern  cities  (see  pi.  2)  indicates  that  many  of  them  were  con- 
temporaneous, and  that  a  few,  namely,  Tikal,  Naranjo,  Palenque, 
and  Copan  were  occupied  approximately  200  years,  a  much  longer 
period  than  any  of  the  others.^  These  four  would  seem  to  have  been 
centers  of  population  for  a  long  time,  and  at  least  three  of  them, 
Tikal,  Palenque,  and  Copan,  attained  considerable  size.  Indeed  they 
may  well  have  been,  like  Chichen  Itza,  Uxmal,  and  Mayapan,  at  a 
later  epoch  in  the  north,  the  seats  of  halach  uincil,  or  overlords,  to 
whom  all  the  surrounding  chiefs  were  tributary.  Geographically 
considered,  the  country  was  well  apportioned  among  these  cities: 
Tikal  dominating  the  north,  Palenque,  the  west,  and  Copan,  the  south. 

The  architecture,  sculpture,  and  hieroglyphic  writing  of  all  the 
southern  centers  is  practically  identical,  even  to  the  borrowing  of 
unessential  details,  a  condition  which  indicates  a  homogeneity  only 
to  be  accounted  for  by  long-continued  and  frequent  intercourse. 
This  characteristic  of  the  culture,  together  with  the  location  and 
contemporaneity  of  its  largest  centers,  suggests  that  originally  the 
southern  territory  was  divided  into  several  extensive  political  divi- 
sions, all  in  close  intercourse  with  one  another,  and  possibly  united 
.  in  a  league  similar  to  that  which  later  united  the  principal  cities  of 
the  north.  ,'  The  unmistakable  priestly  or  religious  character  of  the 
sculptures  in  the  southern  area  clearly  indicates  the  peaceful  temper . 
of  the  people,  and  the  conspicuous  absence  of  warlike  subjects  points 
strongly  to  the  fact  that  the  government  was  a  theocracy,  the  highest 
official  in  the  priesthood  being  at  the  same  time,  by  virtue  of  his 
sacerdotal  rank,  the  highest  civil  authority.  Whether  the  principle 
of  hereditary  succession  determined  or  even  influenced  the  selection 
of  rulers  in  the  south  is  impossible  to  say.  However,  since  the  highest 
offices,  both  executive  and  priestly,  in  the  north  were  thus  filled,  it 
y  may  be  assumed  that  similar  conditions  prevailed  in  the  south,  par- 
ticularly as  the  northern  civihzation  was  but  an  outgrowth  of  the 

1  As  the  result  of  a  trip  to  the  Maya  field  in  the  wiater  of  1914,  the  writer  made  important  discoveries  in 
the  chronology  of  Tikal,  Naranjo,  Piedras  Negras,  Altar  de  Sacrificios,  Quirigua,  and  Seibal.  The  occu- 
pancy of  Tikal  and  Seibal  was  found  to  have  extended  to  10.2.0.0.0;  of  Piedras  Negras  to  9.18.5.0.0; 
of  Naranjo  to  9.19.10.0.0;  and  of  Altar  de  Sacrificios  to  9.14.0.0.0.  (This  new  material  is  not  embodied 
in  pi.  2.) 


16 


BUBEAU  OF  AMEKICAN  ETHNOLOGY 


[BULL.  57 


southern.  There  is  some  ground  for  beheving  that  the  highest  office 
in  the  south  may  have  been  elective,  the  term  being  a  Jiotun^  (1,800 
days),  and  the  choice  restricted  to  the  members  of  a  certain  family. 
The  existence  of  this  restriction,  which  closely  parallels  the  Aztec 
procedure  in  selecting  rulers, ^  rests  on  very  slender  evidence,  how- 
ever, so  far  as  the  Maya  are  concerned  and  is  mentioned  here  simply 
by  way  of  suggestion. 

The  religion  of  the  ancient  Maya  was  polytheistic,  its  pantheon 
containing  about  a  dozen  major  deities  and  a  host  of  lesser  ones.  At 
its  head  stood  Itzamna,  the  father  of  the  gods  and  creator  of  mankind, 
the  Mayan  Zeus  or  Jupiter.  He  was  the  personification  of  the  East, 
the  rising  sun,  and,  by  association,  of  light,  life,  and 
knowledge.  He  was  the  founder  of  the  Maya  civiliza- 
tion, the  first  priest  of  the  Maya  religion,  the  inventor 
of  writing  and  books,  and  the  great  healer.  Whether 
Itzamna  has  been  identified  with  any  of  the  deities  in 
the  ancient  Maya  picture-writings  is  uncertain,  though 
there  are  strong  reasons  for  believing  that  this  deity  is 
the  god  represented  in  figure  1.  His  characteristics 
here  are:  The  aged  face,  Roman  nose,  and  sunken 
toothless  mouth. 

Fig.  1.  Itzamna,  Scarcely  Icss  important  was  the  great  god  Kukulcan, 
Maya'^plntheo^n  ^r  Feathered  Serpent,  the  personification  of  the  West, 
(note  his  name  It  is  related  of  him  that  he  came  into  Yucatan  from 
glyphs,  below).  ^^g^        settled  at  Chichen  Itza,  where  he  ruled 

for  many  years  and  built  a  great  temple.  During  his  sojourn  he  is 
said  to  have  founded  the  city  of  Mayapan,  which  later  became  so 
important.  Finally,  having  brought  the  country  out  of  war  and  dis- 
sension to  peace  and  prosperity,  he  left  by  the  same  way  he  had 
entered,  tarrying  only  at  Chakanputun  on  the  west  coast  to  build 
a  splendid  temple  as  an  everlasting  memorial  of  his  residence  among 
the  people.  After  his  departure  he  was  worshipped  as  a  god  because 
of  what  he  had  done  for  the  public  good.  Kukulcan  was  the  Maya 
counterpart  of  the  Aztec  Quetzalcoatl,  the  Mexican  god  of  light, 
learning,  and  culture.  In  the  Maya  pantheon  he  was  regarded  as 
having  been  the  great  organizer,  the  founder  of  cities,  the  framer  of 
laws,  and  the  teacher  of  their  new  calendar.    Indeed,  his  attributes 

1  As  will  be  explained  in  chapter  V,  the  writer  has  suggested  the  name  hotun  for  the  5  tun,  or  1,800  day, 
period. 

2  Succession  in  the  Aztec  royal  house  was  not  determined  by  primogeniture,  though  the  supreme  office, 
the  tlahtouani,  as  well  as  the  other  high  offices  of  state,  was  hereditary  in  one  family.  On  the  death  of 
the  tlahtouani  the  electors  (four  in  number)  seem  to  have  selected  his  successor  from  among  his  brothers, 
or,  these  failing,  from  among  his  nephews.  Except  as  limiting  the  succession  to  one  family,  primogeniture 
does  not  seem  to  have  obtained;  for  example,  Moetezoma  (Montezuma)  was  chosen  tlahtouani  over  the 
heads  of  several  of  his  older  brothers  because  he  was  thought  to  have  the  best  qualifications  for  that  exalted 
office.  The  situation  may  be  summarized  by  the  statement  that  while  the  supreme  ruler  among  the 
Aztec  had  to  be  of  the  "blood  royal,"  his  selection  was  determined  by  personal  merit  rather  than  by 
primogeniture. 


MORLEY]       IN^TRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


17 


Fig.  2.  Kukulcan, 
God  of  Learning 
(note  his  name 
glyph,  below). 


and  life  history  are  so  human  that  it  is  not  improbable  he  may  have 
been  an  actual  historical  character,  some  great  lawgiver  and  organ- 
izer, the  memory  of  whose  benefactions  lingered  long 
after  death,  and  whose  personality  was  eventually  dei- 
fied. The  episodes  of  his  life  suggest  he  may  have  been 
the  recolonizer  of  Chichen  Itza  after  the  destruction  of 
Chakanputun.  Kukulcan  has  been  identified  by  some 
as  the  ''old  god"  of  the  picture-writings  (fig.  2),  whose 
characteristics  are :  Two  deformed  teeth,  one  protruding 
from  the  front  and  one  from  the  back  part  of  his  mouth, 
and  the  long  tapering  nose.  He  is  to  be  distinguished 
further  by  his  peculiar  headdress. 

The  most  feared  and  hated  of  all  the  Maya  deities 
was  Ahpuch,  the  Lord  of  Death,  God  ''Barebones''  as 
an  early  manuscript  calls  him,  from  whom  evil  and 
especially  death  were  thought  to  come.  He  is  frequently  represented 
in  the  picture-writings  (fig.  3),  usually  in  connection  with  the  idea  of 
death.  He  is  associated  with  human  sacrifice,  suicide 
by  hanging,  death  in  childbirth,  and  the  beheaded 
captive.  His  characteristics  are  typical  and  unmis- 
takable. His  head  is  the  fleshless  skull,  showing  the 
truncated  nose,  the  grinning  teeth,  and  fleshless  lower 
jaw,  sometimes  even  the  cranial  sutures  are  por- 
trayed. In  some  places  the  ribs  and  vertebrae  are 
shown,  in  others  the  body  is  spotted  black  as  if  to 
suggest  the  discoloration  of  death.  A  very  constant 
symbol  is  the  stiff  feather  collar  with  small  bells  at- 
These  bells  also  appear  as  ornaments  on  the 
head,  arms,  and  ankles.  The  to  us  familiar  crossbones 
were  also  another  Maya  death  symbol.  Even  the  hieroglyph  of  this 
god  (fig.  3)  suggests  the  dread  idea  for  which  he  stood.  Note  the 
eye  closed  in  death. 

Closely  associated  with  the  God  of  Death  is  the  God  of 
War,  who  probably  stood  as  well  for  the  larger  idea  of 
death  by  violence.  He  is  characterized  (fig.  4)  by  a 
black  line  painted  on  his  face,  sometimes  curving,  some- 
times straight,  supposed  to  be  symboHcal  of  war  paint, 
or,  according  to  others,  of  his  gaping  wounds.  He  ap- 
pears in  the  picture-writings  as  the  Death  God's  com- 
panion. He  presides  with  him  over  the  body  of  a  sacri- 
ficial victim,  and  again  follows  him  applying  torch  and 
knife  to  the  habitations  of  man.  His  hieroglyph  shows 
as  its  characteristic  the  line  of  black  paint  (fig.  4). 

Another  unpropitious  deity  was  Ek  Ahau,  the  Black  Captain,  also  a 
war  god,  being  represented  (fig.  5)  in  the  picture-writings  as  armed 
43508°— Bull.  57—15  2 


Fig.  3.    Ahpuch,  God 
of  Death  (note  his  tached. 
name  glyphs,below). 


Fig.  4.  The  God  of 

War  (note  his  name 
glyph,  below). 


18 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


Fig.  5.  EkAhau, 
the  Black  Cap- 
tain, war  deity 


with  a  spear  or  an  ax.  It  was  said  of  him  that  he  was  a  very  great 
and  very  cruel  warrior,  who  commanded  a  band  of  seven  black- 
amoors like  himself.  He  is  characterized  by  his  black  color,  his 
drooping  lower  lip,  and  the  two  curved  lines  at  the  right  of  his  eye. 
His  hieroglyph  is  a  black  eye  (fig.  5). 

Contrasted  with  these  gods  of  death,  violence,  and  de- 
struction was  the  Maize  God,  Yum  Kaax,  Lord  of  the 
Harvest  Fields  (fig.  6).    Here  we  have  one  of  the  most 
important  figures  in  the  whole  Maya  pantheon,  the  god 
of  husbandry  and  the  fruits  of  the  earth,  of  fertility  and 
prosperity,  of  growth  and  plenty.    The  Maize  God  was 
as  well  disposed  toward  mankind  as  Ahpuch  and  his 
companions  were  unpropitious.    In  many  of  the  pic- 
ture-writings Yum  Kaax  is  represented  as  engaged  in 
agricultural  pursuits.    He  is  portrayed  as  having  for 
his  head-dress  a  sprouting  ear  of  corn  surrounded  by 
(note  his  name  leavos.  Symbolic  of  growth,  for  which  he  stands.  Even 
glyph,  below).         hieroglyph  of  this  deity  (fig.  6)  embodies  the  same 
idea,  the  god's  head  merging  into  the  conventionalized  ear  of  corn 
surrounded  by  leaves. 

Another  important  deity  about  whom  little  or  nothing  is  known 
was  Xaman  Ek,  the  North  Star.  He  is  spoken  of  as  the  ''guide  of 
the  merchants,"  and  in  keeping  with  that  character  is  associated  in 
the  picture-writings  with  symbols  of  peace  and  plenty. 
His  one  characteristic  seems  to  be  his  curious  head, 
which  also  serves  as  his  name  hieroglyph  (fig.  7). 

Other  Maya  deities  were:  Ixchel,  the  Rainbow, 
consort  of  Itzamna  and  goddess  of  childbirth  and 
medicine;  Ixtab,  patroness  of  hunting  and  hanging; 
Ixtubtun,  protectress  of  jade  cutters;  Ixchebelyax, 
the  inventress  of  painting  and  color  designing  as  ap- 
plied to  fabrics. 

Although  the  deities  above  described  represent  only 
a  small  fraction  of  the  Maya  pantheon,  they  include, 
beyond  all  doubt,  its  most  important  members,  the 
truly  great,  who  held  the  powers  of  life  and  death, 
peace  and  war,  plenty  and  famine — who  were,  in  short,  the  arbiters 
of  human  destiny. 

The  Maya  conceived  the  earth  to  be  a  cube,  which  supported  the 
celestial  vase  resting  on  its  four  legs,  the  four  cardinal  points.  Out 
of  this  grew  the  Tree  of  Life,  the  flowers  of  which  were  the  immortal 
principle  of  man,  the  soul.  Above  hung  heavy  clouds,  the  fructi- 
fying waters  upon  which  all  growth  and  life  depend.  The  religion 
was  dualistic  in  spirit,  a  constant  struggle  between  the  powers  of 


Fig.  6.  Yum  Kaax, 
Lord  of  the  liar- 
vest  (note  his  name 
glyph,  below). 


MORLET]       INTKODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


19 


Fig 


7.  Xaman  Ek, 
the  North  Star  God 
(note  his  name 
glyph,  below). 


light  and  of  darkness.  On  one  side  were  arrayed  the  gods  of  plenty, 
peace,  and  life;  on  the  other  those  of  want,  war,  and  destruction; 
and  between  these  two  there  waged  an  unending  strife  for  the  control 
of  man.  This  struggle  between  the  powers  of  hght  and  darlaiess  is 
graphically  portrayed  in  the  picture-writings .  Where 
the  God  of  Life  plants  the  tree.  Death  breaks  it  in 
twain  (fig.  8) ;  where  the  former  offers  food,  the  latter 
raises  an  empty  vase  symbolizing  famine;  where  one 
builds,  the  other  destroys.  The  contrast  is  complete, 
the  conflict  eternal. 

The  Maya  beheved  in  the  immortahty  of  the  soul 
and  in  a  spiritual  life  hereafter.  As  a  man  lived  in  this 
world  so  he  was  rewarded  in  the  next.  The  good  and 
righteous  went  to  a  heaven  of  material  delights,  a 
place  where  rich  foods  never  failed  and  pain  and  sor- 
row were  unknown.  The  wicked  were  consigned  to  a 
hell  called  Mitnal,  over  which  ruled  the  archdemon 
Hunhau  and  his  minions ;  and  here  in  hunger,  cold,  and  exhaustion  they 
suffered  everlasting  torment.  The  materialism  of  the  Maya  heaven 
and  hell  need  not  surprise,  nor  lower  our  estimate  of  their  civilization. 
Similar  reahstic  conceptions  of  the  hereafter  have  been  entertained 
by  peoples  much  higher  in  the  cultural  scale  than  the  Maya. 

Worship  doubtless  was  the  most  important  feature  of  the  Maya 
scheme  of  existence,  and  an  endless  succession  of  rites  and  ceremonies 

was  considered  necessary  to  retain  the 
sympathies  of  the  good  gods  and  to  pro- 
pitiate the  malevolent  ones.  Bishop 
Landa  says  that  the  aim  and  object  of 
all  Maya  ceremonies  were  to  secure  three 
things  only :  Health,  life,  and  sustenance ; 
modest  enough  requests  to  ask  of  any 
faith.  The  first  step  in  aU  Maya  reli- 
gious rites  was  the  expulsion  of  the  evil 
spirits  from  the  midst  of  the  worshipers.  This  was  accomplished 
sometimes  by  prayers  and  benedictions,  set  formulae  of  proven 
efficacy,  and  sometimes  by  special  sacrifices  and  offerings. 

It  would  take  us  too  far  afield  to  describe  here  even  the  more 
important  ceremonies  of  the  Maya  reUgion.  Their  number  was  Uter- 
ally  legion,  and  they  answered  almost  every  contingency  within  the 
range  of  human  experience.  First  of  all  were  the  ceremonies  dedi- 
cated to  special  gods,  as  Itzamna,  Kukulcan,  and  Ixchel.  Probably 
every  deity  in  the  pantheon,  even  the  most  insignificant,  had  at  least 
one  rite  a  year  addressed  to  it  alone,  and  the  aggregate  must  have 
made  a  very  considerable  number.  In  addition  there  were  the  annual 
feasts  of  the  ritualistic  year  brought  around  by  the  ever-recurring 


Fig.  8.   Conflict  between  the  Gods  of  Life 
and  Death  (Kukulcan  and  Ahpuch). 


20 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


seasons.  Here  may  be  mentioned  the  numerous  ceremonies  incident 
to  the  beginning  of  the  new  year  and  the  end  of  the  old,  as  the  renewal 
of  household  utensils  and  the  general  renovation  of  all  articles,  which 
took  place  at  this  time;  the  feasts  of  the  various  trades  and  occupa- 
tions— the  hunters,  fishers,  and  apiarists,  the  farmers,  carpenters,  and 
potters,  the  stonecutters,  wood  carvers,  and  metal  workers — each 
guild  having  its  own  patron  deity,  whose  services  formed  another  large 
group  of  ceremonials.  A  third  class  comprised  the  rites  of  a  more 
personal  nature,  those  connected  with  baptism,  confession,  marriage, 
setting  out  on  journeys,  and  the  like.  Finally,  there  was  a  fourth 
group  of  ceremonies,  held  much  less  frequently  than  the  others,  but 
of  far  greater  importance.  Herein  fall  the  ceremonies  held  on  extra- 
ordinary occasions,  as  famine,  drought,  pestilence,  victory,  or  defeat, 
which  were  probably  solemnized  by  rites  of  human  sacrifice. 

The  direction  of  so  elaborate  a  system  of  worship  necessitated  a 
numerous  and  highly  organized  priesthood.  At  the  head  of  the 
hierarchy  stood  the  hereditary  high  priest,  or  ahaucan  mai,  a  func- 
tionary of  very  considerable  power.  Although  he  had  no  actual 
share  in  the  government,  his  influence  was  none  the  less  far-reaching, 
since  the  highest  lords  sought  his  advice,  and  deferred  to  his  judgment 
in  the  administration  of  their  affairs.  They  questioned  him  con- 
cerning the  will  of  the  gods  on  various  points,  and  he  in  response 
framed  the  divine  replies,  a  duty  which  gave  him  tremendous  power 
and  authority.  In  the  ahuacan  mai  was  vested  also  the  exclusive 
right  to  fill  vacancies  in  the  priesthood.  He  examined  candidates 
on  their  knowledge  of  the  priestly  services  and  ceremonies,  and  after 
their  appointment  directed  them  in  the  discharge  of  their  duties. 
He  rarely  officiated  at  sacrifices  except  on  occasions  of  the  greatest 
importance,  as  at  the  principal  feasts  or  in  times  of  general  need. 
His  office  was  maintained  by  presents  from  the  lords  and  enforced 
contributions  from  the  priesthood  throughout  the  country. 

The  priesthood  included  within  its  ranks  women  as  well  as  men. 
The  duties  were  highly  specialized  and  there  were  many  different 
ranks  and  grades  in  the  hierarchy.  The  chilan  was  one  of  .  the  most 
important.  This  priest  was  carried  upon  the  shoulders  of  the  people 
when  he  appeared  in  pubUc.  He  taught  their  sciences,  appointed 
the  holy  days,  healed  the  sick,  offered  sacrifices,  and  most  important 
of  all,  gave  the  responses  of  the  gods  to  petitioners.  The  ahuai  chac 
was  a  priest  who  brought  the  rains  on  which  the  prosperity  of  the 
country  was  wholly  dependent.  The  ah  macik  conjured  the  winds; 
the  ahful  caused  sickness  and  induced  sleep:  the  ahuai  xihalha 
communed  with  the  dead.  At  the  bottom  of  the  ladder  seems  to  have 
stood  the  nacon,  whose  duty  it  was  to  open  the  breasts  of  the  sacrificed 
victims.  An  important  elective  office  in  each  community  was  that 
held  by  the  chac,  or  priest's  assistant.    These  officials,  of  which  there 


„0K...]      INTRODUCTIOK  TO  STUDY  OF  MAYA  HIEEOGLYPHS  21 

w.re  four   were  elected  from  the  nucteelob,  or  village  wise  men. 

iyH-nrf-  ,ri:^t7Stf 

S  *ort w..  th.  fou.d..io.  upon  whict  U>.  .1  0.. 

Maya  civilization  was  reared. 


Chapter  II.  THE  MAYA  HIEROGLYPHIC  WRITING 


The  inscriptions  herein  described  are  found  throughout  the  region 
formerly  occupied  by  the  Maya  people  (pi.  1),  though  by  far  the 
greater  number  have  been  discovered  at  the  southern,  or  older,  sites. 
This  is  due  in  part,  at  least,  to  the  minor  r61e  played  by  sculpture 
as  an  independent  art  among  the  northern  Maya,  for  in  the  north 
architecture  gradually  absorbed  in  its  decoration  the  sculptural 
activity  of  the  people  which  in  the  south  had  been  applied  in  the 
making  of  the  hieroglyphic  monuments. 

C  /       The  materials  upon  which  the  Maya  glyphs  are  presented 

a       are  stone,  wood,  stucco,  bone,  shell,  metal,  plaster,  pottery, 
r-^     and  fiber-paper;  the  first-mentioned,  however,  occurs  more 
(_J     frequently  than  all  of  the  others  combined.    Texts  have  been 
6        found  carved  on  the  wooden  lintels  of  Tikal,  molded  in  the 
stucco  reliefs  of  Palenque,  scratched  on  shells  from  Copan  and 

□ Belize,  etched  on  a  bone  from  Wild  Cane  Key,  British  Hon- 
duras, engraved  on  metal  from  Chichen  Itza,  drawn  on  the 
Fig    9    pl^ster-covcred  walls  of  Kabah,  Chichen  Itza,  and  Uxmal,  and 
Outlines  painted  in  fiber-paper  books.    All  of  these,  however,  with  the 
glyphs^  exception  of  the  first  and  the  last  (the  inscriptions  on  stone 
a,  6,  lu  and  the  fiber-paper  books  or  codices)  just  mentioned,  occur  so 
d^ces  T  rarely  that  they  may  be  dismissed  from  present  consideration, 
in  the      The  stoucs  bearing  inscriptions  are  found  in  a  variety  of 
Mons"^    shapes,  the  commonest  being  the  monolithic  shafts  or  slabs 
known  as  stelse,.    Some  of  the  shaft-stelse  attain  a  height  of 
twenty-six  feet  (above  ground) ;  these  are  not  unlike  roughly  squared 
obelisks,  with  human  figures  carved  on  the  obverse  and  the  reverse, 
and  glyphs  on  the  other  faces.    Slab-stelse,  on  the  other  hand,  are 
shorter  and  most  of  them  bear  inscriptions  only  on  the  reverse.  Fre- 
quently associated  with  these  stelae  are  smaller  monoliths  known  as 
'^altars,"  which  vary  greatly  in  size,  shape,  and  decoration,  some  bear- 
ing glyphs  and  others  being  without  them. 

The  foregoing  monuments,  however,  by  no  means  exhaust  the  list 
of  stone  objects  that  bear  hieroglyphs.  As  an  adjunct  to  architecture 
inscriptions  occur  on  wall-slabs  at  Palenque,  on  lintels  at  Yaxchilan 
and  Piedras  Negras,  on  steps  and  stairways  at  Copan,  and  on  piers 
and  architraves  at  Holactun;  and  these  do  not  include  the  great 
number  of  smaller  pieces,  as  inscribed  jades  and  the  like.  Most  of 
the  glyphs  in  the  inscriptions  are  square  in  outline  except  for  rounded 
corners  (fig.  9,  c).  Those  in  the  codices,  on  the  other  hand,  approx- 
imate more  nearly  in  form  rhomboids  or  even  ovals  (fig.  9,  a,  h). 
This  difference  in  outline,  however,  is  only  superficial  in  significance 
and  involves  no  corresponding  difference  in  meaning  between  other- 
22 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


23 


wise  identical  glyplis  •  it  is  due  entirely  to  the  mechanical  dissimilarity 
of  the  two  materials.  Disregarding  this  consideration  as  unessential, 
we  may  say  that  the  glyphs  in  both  the  inscriptions  and  the  codices 
belong  to  one  and  the  same  system  of  writiag,  and  if  it  were  possible 
to  read  either,  the  other  could  no  longer  withhold  its  meaning  from  us. 

In  Maya  inscriptions  the  glyphs  are  arranged  in  parallel  columns, 
which  are  to  be  read  two  columns  at  a  time,  beginning  with  the  upper- 
most glyph  in  the  left-hand  column,  and  then  from  left  to  right  and 
top  to  bottom,  ending  with  the  lowest  glyph  in  the  second  column. 
Then  the  next  two  columns  are  read  in  the  same  order,  and  so  on. 
In  reading  glyphs  in  a  horizontal  band,  the  order  is  from  left  to  right 
in  pairs.  The  writer  knows  of  no  text  in  which  the  above  order  of 
reading  is  not  followed. 

A  brief  examination  of  any  Maya  text,  from  either  the  inscriptions 
or  the  codices,  reveals  the  presence  of  certain  elements  which  occur 
repeatedly  but  in  varying  combinations.  The  apparent  multiplicity 
of  these  combinations  leads  at  first  to  the  conclusion  that  a  OTeat 
number  of  signs  were  employed  in  Maya  writing,  but  closer  study  will 


a  h  c  d  e 

Fig.  10.   Examples  of  glyph  elision,  showing  elimination  of  all  parts  except  essential  element  (here,  the 

crossed  bands). 

show  that,  as  compared  with  the  composite  characters  or  glyphs 
proper,  the  simple  elements  are  few  in  number.  Says  Doctor 
Brinton  (1894  b:  p.  10)  in  this  connection:  ''If  we  positively  knew  the 
meaning  .  .  of  a  hundred  or  so  of  these  simple  elements,  none  of 
the  inscriptions  could  conceal  any  longer  from  us  the  general  tenor 
of  its  contents."  Unfortunately,  it  must  be  admitted  that  but  little 
advance  has  been  made  toward  the  solution  of  this  problem,  perhaps 
because  later  students  have  distrusted  the  highly  fanciful  results 
achieved  by  the  earlier  writers  who  interpreted"  these  simple 
elements." 

Moreover,  there  is  encountered  at  the  very  outset  in  the  study  of 
these  elements  a  condition  which  renders  progress  slow  and  results 
uncertain.  In  Egyptian  texts  of  any  given  period  the  simple  pho- 
netic elements  or  signs  are  unchanging  under  all  conditions  of  com- 
position. Like  the  letters  of  our  own  alphabet,  they  never  vary  and 
may  be  recognized  as  unfailingly.  On  the  other  hand,  m  Maya  texts 
each  glyph  is  in  itself  a  finished  picture,  dependent  on  no  other  for 
its  meaning,  and  consequently  the  various  elements  entering  into  it 
undergo  very  considerable  modifications  in  order  that  the  resulting 
composite  character  may  not  only  be  a  balanced  and  harmonious  de- 


24 


BUEEAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


sign,  but  also  may  exactly  fill  its  allotted  space.  All  such  modifications 
probably  in  no  way  affect  the  meaning  of  the  element  thus  mutilated. 

The  element  shown  in  figure  10,  a~e  is  a  case  in  pomt.  In  a  and  h 
we  have  what  may  be  called  the  normal  or  regular  forms  of  this 
element.  In  c,  however,  the  upper  arm  has  been  omitted  for  the  sake 
of  symmetry  in  a  composite  glyph,  while  in  d  the  lower  arm  has  been 
left  out  for  want  of  space.  Finally  in  e  both  arms  have  disappeared 
g  and  the  element  is  reduced  to  the  sign  (*),  which  we  may  con- 
*  elude,  therefore,  is  the  essential  characteiistic  of  this  glyph,  par- 
ticularly since  there  is  no  regularity  in  the  treatment  of  the  arms  in  the 
normal  forms.  This  suggests  another  point  of  the  utmost  importance, 
namely,  the  determination  of  the  essential  elements  of  Maya  glyphs. 
The  importance  of  this  point  lies  in  the  fact  that  great  license  was 
permitted  in  the  treatment  of  accessory  elements  so  long  as  the 
essential  element  or  elements  of  a  glyph  could  readily  be  recognized 
as  such.    In  this  way  may  be  explained  the  use  of  the  so-called 


m  n 

Fig.  n.    Normal-form  and  head-variant  glyphs,  showing  retention  of  essential  element  in  each, 

''head"  variants,  in  which  the  outline  of  the  glyph  was  represented 
as  a  human  or  a  grotesque  head  modified  in  some  way  by  the  essential 
element  of  the  intended  form.    The  first  step  in  the  development  of 
head  variants  is  seen  m  figure  11,  a,  I,  in  which  the  entire  glyph  a  is 
used  as  a  headdress  in  glyph  6,  the  meaning  of  the  two  forms  remain- 
ing identical.    The  next  step  is  sho\vn  in  the  same  figure,  c  and  d,  in 
which  the  outline  of  the  entire  glyph  c  has  been  changed  to  form  the 
grotesque  head  d,  though  in  both  glyphs  the  essential  elements  are 
the  same.    A  further  development  was  to  apply  the  essential  element 
(g)  (**)  of  e  to  the  head  in  /,  giving  rise  to  a  head  variant, 
**       t     the  meaning  of  which  suffered  no  corresponding  change. 
The  element  (f)  in  figure  11,  g,  has  been  reduced  in  size  in  Ti, 
^  ^TTT?v-v  though  the  other  two  essential   elements   remain  un- 
j  changed.    A  final  step  appears  in  i  and  j,  where  in 

j  the  position  of  one  of  the  two  essential  elements  of  i  (tt)  and 
the  form  of  the  other  (t)  have  been  changed.     These  variants 


MOELEY]      INTRODUCTION  TO  STUDY  OP  MAYA  HIEROGLYPHS 


25 


are  puzzling  enough  when  the  essential  characteristics  and  meaning 
of  a  glyph  have  been  determined,  but  when  both  are  imknown  the 
problem  is  indeed  knotty.  For  example,  it  would  seem  as  a  logical 
deduction  from  the  foregoing  examples,  that  I  of  figure  11  is  a  ''head" 
variant  of  Jc;  and  similarly  n  might  be  a  ''head"  variant  of  m,  but 
here  we  are  treading  on  uncertain  ground,  as  the  meanings  of  these 
forms  are  unknown. 

Nor  is  this  feature  of  Maya  writing  (i.  e.,  the  presence  of  "head 
variants")  the  only  pitfall  which  awaits  the  beginner  who  attempts 
to  classify  the  glyphs  according  to  their  appearance.  In  some  cases 
two  entirely  dissimilar  forms  express  exactly  the  same  idea.  For 
example,  no  two  glyphs  could  differ  more  in  appearance  than  a  and  h, 
figure  12,  yet  both  of  these  forms  have  the  same  meaning.  This 
is  true  also  of  the  two  glyphs  c  and  d,  and  e  and/.  The  occurrence  of 
forms  so  absolutely  unlike  in  appearance,  yet  identical  in  meaning, 
greatly  complicates  the  problem  of  glyph  identification.  Indeed, 
identity  in  both  meaning  and  use  must  be  clearly  estabHshed  before 
we  can  recognize  as  variants  of  the  same  glyph,  forms  so  dissimilar 
as  the  examples  above  given.  Hence,  because  their  meanings  are 
unknown  we  are  unable  to  identify  g  and  Ji,  figure  12,  as  synonyms, 


ah  c  d  e  f  g  h 

Fig.  12.   Normal-form  and  head- variant  glyphs,  showing  absence  of  common  essential  element. 


notwithstanding  the  fact  that  their  use  seems  to  be  identical,  li 
occurring  in  two  or  three  texts  under  exactly  the  same  conditions 
as  does  g  in  all  the  others. 

A  further  source  of  error  in  glyph  identification  is  the  failure  to 
recognize  variations  due  merely  to  individual  peculiarities  of  style, 
which  are  consequently  unessential.  Just  as  handwriting  differs 
in  each  individual,  so  the  delineation  of  glyphs  differed  among  the 
ancient  Maya,  though  doubtless  to  a  lesser  extent.  In  extreme 
cases,  however,  the  differences  are  so  great  that  identification  of 
variants  a^  forms  of  one  and  the  same  glyph  is  difficult  if  indeed  not 
impossible.  Here  also  are  to  be  included  variations  due  to  diff  erences 
in  the  materials  upon  which  the  glyphs  are  delineated,  as  well  as  those 
arising  from  careless  drawing  and  actual  mistakes. 

The  foregoing  difficulties,  as  well  as  others  which  await  the  student 
who  would  classify  the  Maya  glyphs  according  to  form  and  appear- 
ance, have  led  the  author  to  discard  this  method  of  classification  as 
unsuited  to  the  purposes  of  an  elementary  work.  Though  a  problem 
of  first  importance,  the  analysis  of  the  simple  elements  is  far  too 
complex  for  presentation  to  the  beginner,  particularly  since  the 


26 


BUEEAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


greatest  diversity  of  opinion  concerning  them  prevails  among  those 
who  have  studied  the  subject,  scarcely  any  two  agreeing  at  any  one 
point;  and  finally  because  up  to  the  present  time  success  in  reading 
Maya  writing  has  not  come  through  this  channel. 

The  classification  followed  herein  is  based  on  the  general  meaning 
of  the  glyphs,  and  therefore  has  the  advantage  of  being  at  least  self- 
explanatory.  It  divides  the  glyphs  into  two  groups:  (1)  Astronomi- 
cal, calendary,  and  numerical  signs,  that  is,  glyphs  used  in  counting 
time;  and  (2)  glyphs  accompanying  the  preceding,  which  have  an 
explanatory  function  of  some  sort,  probably  describing  the  nature  of 
the  occasions  which  the  first  group  of  glyphs  designate. 

According  to  this  classification,  the  great  majority  of  the  glyphs 
whose  meanings  have  been  determined  fall  into  the  first  group,  and 
those  whose  meanings  are  still  unknown  into  the  second.  This  is 
particularly  true  of  the  inscriptions,  in  which  the  known  glyphs 
practically  all  belong  to  the  first  group.  In  the  codices,  on  the  other 
hand,  some  little  progress  has  made  been  in  reading  glyphs  of  the 
second  group.  The  name-glyphs  of  the  principal  gods,  the  signs  for 
the  cardinal  points  and  associated  colors,  and  perhaps  a  very  few 
others  may  be  mentioned  in  this  connection.^ 

Of  the  unknown  glyphs  in  both  the  inscriptions  and  the  codices,  a 
part  at  least  have  to  do  with  numerical  calculations  of  some  kind,  a  fact 
which  relegates  such  glyphs  to  the  first  group.  The  author  believes 
that  as  the  reading  of  the  Maya  glyphs  progresses,  more  and  more 
characters  wiU  be  assigned  to  the  first  group  and  fewer  and  fewer  to 
the  second.  In  the  end,  however,  there  will  be  left  what  we  may 
perhaps  call  a  ''textual  residue,"  that  is,  those  glyphs  which  explain 
the  nature  of  the  events  that  are  to  be  associated  with  the  correspond- 
ing chronological  parts.  It  is  here,  if  anywhere,  that  fragments  of 
Maya  history  will  be  found  recorded,  and  precisely  here  is  the  richest 
field  for  future  research,  since  the  successful  interpretation  of  this 
^'textual  residue"  will  alone  disclose  the  true  meaning  of  the  Maya 
writings. 

Three  principal  theories  have  been  advanced  for  the  interpretation 
of  Maya  writing: 

1.  That  the  glyphs  are  phonetic,  each  representing  some  sound, 
and  entirely  dissociated  from  the  representation  of  any  thought  or  idea. 

2.  That  the  glyphs  are  ideographic,  each  representing  in  itself  some 
complete  thought  or  idea. 

3.  That  the  glyphs  are  both  phonetic  and  ideographic,  that  is,  a 
combination  of  1  and  2. 

It  is  apparent  at  the  outset  that  the  first  of  these  theories  can  not 
be  accepted  in  its  entirety ;  for  although  there  are  undeniable  traces 


1  There  can  be  no  doubt  that  Forstemann  has  identified  the  sign  for  the  planet  Venus  and  possibly  a 
few  others.   (See  Forstemann,  1906:  p.  116.) 


M OR LEY] 


INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


27 


of  phoneticism  among  the  Maya  glyphs,  all  attempts  to  reduce  them 
to  a  phonetic  system  or  alphabet,  which  will  interpret  the  writing, 
have  signally  failed.  The  first  and  most  noteworthy  of  these  so-called 
''Maya  alphabets,'^  because  of  its  genuine  antiquity,  is  that  given  by 
Bishop  Landa  in  his  invaluable  Relacion  de  las  cosas  de  Yucatan,  fre- 
quently cited  in  Chapter  I.  Writing  in  the  year  1565,  within  25 
years  of  the  Spanish  Conquest,  Landa  was  able  to  obtain  characters 
for  27  sounds,  as  follows :  Three  a's,  two  ¥s,  c,  t,  e,  Ti,  i,  ca,  Ic,  two  Vs, 
m,  n,  two  o's,  'p'p,  p,  cu,  leu,  two  x^s,  two  v^s,  z.  This  alphabet,  which 
was  first  published  in  1864  by  Abb6  Brasseur  de  Bourbourg  (see 
Landa,  1864),  was  at  once  heralded  by  Americanists  as  the  long- 
awaited  key  which  would  unlock  the  secrets  of  the  Maya  writing. 
Unfortunately  these  confident  expectations  have  not  been  realized, 
and  all  attempts  to  read  the  glyphs  by  means  of  this  alphabet  or  of 
any  of  the  numerous  others^  which  have  appeared  since,  have  com- 
pletely broken  down. 

This  failure  to  establish  the  exclusive  phonetic  character  of  the 
Maya  glyphs  has  resulted  in  the  general  acceptance  of  the  second 
theory,  that  the  signs  are  ideographic.  Doctor  Briaton  (1894  b :  p.  14) , 
however,  has  pointed  out  two  facts  deducible  from  the  Landa  alpha- 
bet which  render  impossible  not  only  the  complete  acceptance  of  this 
second  theory  but  also  the  absolute  rejection  of  the  first:  (1)  That  a 
native  writer  was  able  to  give  a  written  character  for  an  unfamiliar 
sound,  a  sound,  moreover,  which  was  without  meaning  to  him,  as, 
for  example,  that  of  a  Spanish  letter;  and  (2)  that  the  characters 
he  employed  for  this  purpose  were  also  used  in  the  native  writings. 
These  facts  Doctor  Brinton  regards  as  proof  that  some  sort  of 
phonetic  writing  was  not  unknown,  and,  indeed,  both  the  inscrip- 
tions and  the  codices  establish  the  truth  of  this  contention.  For 
example,  the  siga  in  a,  figure  13,  has  the  phonetic  value  ^m,  and 
the  sign  in  h  the  phonetic  value  yax.  In  the  latter  glyph,  however, 
only  the  upper  part  (reproduced  in  c)  is  to  be  regarded  as  the  essen- 
tial element.  It  is  strongly  indicative  of  phoneticism  therefore  to 
find  the  sound  yaxMn,  a  combination  of  these  two,  expressed  by  the 
sign  found  in  d.  Similarly,  the  character  representing  the  phonetic 
value  Mn  is  found  also  as  an  element  in  the  glyphs  for  the  words  lilcin 

1  Brasseur  de  Bourbourg,  the  "discoverer"  of  Landa's  manuscript,  added  several  signs  of  his  own 
invention  to  the  original  Landa  alphabet.  See  his  introduction  to  the  Codex  Troano  published  by  the 
French  Government.  Leon  de  Rosny  published  an  alphabet  of  29  letters  with  numerous  variants. 
Later  Dr.  F.  Le  Plongeon  defined  23  letters  with  variants  and  made  elaborate  interpretations  of  the  texts 
with  this  "alphabet"  as  his  key.  Another  alphabet  was  that  proposed  by  Dr.  Hilbome  T.  Cresson,  which 
included  syllables  as  well  as  letters,  and  with  which  its  originator  also  essayed  to  read  the  texts.  Scarce 
worthy  of  mention  are  the  alphabet  and  volume  of  interlinear  translations  from  both  the  inscriptions 
and  the  codices  published  by  F.  A.  de  la  Rochefoucauld.  This  is  very  fantastic  and  utterly  without  value 
unless,  as  Doctor  Brinton  says,  it  be  taken  "as  a  warning  against  the  intellectual  aberrations  to  which 
students  of  these  ancient  mysteries  seem  peculiarly  prone."  The  late  Dr.  Cyrus  Thomas,  of  the  Bureau 
of  American  Ethnology,  was  the  last  of  those  who  endeavored  to  interpret  the  Maya  texts  by  means  of 
alphabets,  though  he  was  perhaps  the  best  of  them  all,  much  of  his  work  in  this  particular  respect  will 
not  stand. 


28 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL,  .j" 


aad  chikin  (sec  e  and/,  respectively,  fig.  13),  each  of  which  has  Tcin  as 
its  last  syllabl(\  Again,  th(^  phonetic  value  tun  is  expressed  by  the 
gljrph  in  g,  and  the  sound  ca  (c  hard)  by  the  sign  h.  The  somid  Icatun 
is  represented  by  the  character  in  i,  a  combination  of  these  two. 
Sometimes  the  glyph  for  this  same  sound  takes  the  form  of  j,  the  fish 
element  in  Ic  replacing  the  comblike  element  h.  Far  from  destroy- 
ing the  phonetic  character  of  this  composite  glyph,  however,  this 
variant  Jc  in  reality  strengthens  it,  since  in  Maya  the  word  for  fish  is 
cay  (c  hard)  and  consequently  the  variant  reads  caytun,  a  close  pho- 
netic approximation  of  Icatun.  The  remaining  element  of  this  glyph 
(Z)  has  the  value  cauac,  the  first  syllable  of  which  is  also  expressed  by 
either  h  or  Ic,  figure  13.  Its  use  in  i  and  j  probably  may  be  regarded 
as  but  a  further  emphasis  of  the  phonetic  character  of  the  glyph. 

It  must  be  remembered,  however,  that  all  of  the  above  glyphs  have 
meanings  quite  independent  of  their  phoTietic  values,  that  primarily 


g  hi  j  k 

Fig.  13.    Glyphs  built  up  on  a  phonetic  basis. 


their  function  was  to  convey  ideas,  and  that  only  secondarily  were 
they  used  in  their  phonetic  senses. 

If  neither  the  phonetic  nor  the  ideographic  character  of  the  glyphs 
can  be  wholly  admitted,  what  then  is  the  true  nature  of  the  Maya 
writing?  The  theory  now  most  generally  accepted  is,  that  while 
chiefly  ideographic,  the  glyphs  are  sometimes  phonetic,  and  that 
although  the  idea  of  a  glyphic  alphabet  must  finally  be  abandoned, 
the  phonetic  use  of  syllables  as  illustrated  above  must  as  surely  be 
recognized. 

This  kind  of  writing  Doctor  Brinton  has  called  iJconomatic,  more 
familiarly  known  to  us  under  the  name  of  rebus,  or  puzzle  writing. 
In  such  writing  the  characters  do  not  indicate  the  ideas  of  the  objects 
which  they  portray,  but  only  the  sounds  of  their  names,  and  are 
used  purely  in  a  phonetic  sense,  like  the  letters  of  the  alphabet. 
For  example,  the  rebus  in  figure  14  reads  as  follows:  ''I  believe  Aunt 
Rose  can  well  bear  all  for  you."  The  picture  of  the  eye  recalls  not 
the  idea  ''eye"  but  the  sound  of  the  word  denoting  this  object,  which 
is  also  the  sound  of  the  word  for  the  first  person  singular  of  the  per- 


MORLET]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


29 


sonal  pronoun  I.  Again,  the  picture  of  a  bee  does  not  represent  the 
idea  of  that  insect,  but  stands  for  the  sound  of  its  name,  which 
used  with  a  leaf  indicates  the  sound  ''beeleaf/^  or  in  other  words, 
'^believe."  1 

It  has  long  been  known  that  the  Aztec  employed  ikonomatic  char- 
acters in  their  writing  to  express  the  names  of  persons  and  places, 
though  this  practice  does  not  seem  to  have  been  extended  by  them 
to  the  representation  of  abstract  words.  The  Aztec  codices  contain 
many  glyphs  which  are  to  be  interpreted  ikonomatically,  that  is,  like 
our  own  rebus  writing.  For  example  in  figure  15,  a,  is  shown  the 
Aztec  hieroglyph  for  the  town  of  Toltitlan,  a  name  which  means 
'^near  the  place  of  the  rushes."  The  word  toUin  means  place  of 
the  rushes,"  but  only  its  first  syllable  tol  appears  in  the  word  Toltitlan. 
This  syllable  is  represented  in  a  by  several  rushes.    The  v^ovd  tetlan 


Fig.  14.   A  rebus.   Aztec,  and  probably  Maya,  personal  and  place  names  were  written  in  a  corresponding 

manner. 


means  '^near  something"  audits  second  syllable  tlan  is  found  also 
in  the  word  tlantli,  meaning  'Heeth."  In  a  therefore,  the  addition 
of  the  teeth  to  the  rushes  gives  the  word  Toltitlan.  Another  example 
of  this  kind  of  writing  is  given  in  figure  15,  h,  where  the  hieroglyph  for 
the  town  of  Acatzinco  is  shown.  This  word  means  'Hhe  little  reed 
grass,"  the  diminutive  being  represented  by  the  syllable  tzinco. 
The  reed  grass  (acatl)  is  shown  by  the  pointed  leaves  or  spears  which 
emerge  from  the  lower  part  of  a  human  figure.  This  part  of  the 
body  was  called  by  the  Aztecs  tzinco,  and  as  used  here  expresses  merely 
the  sound  tzinco  in  the  diminutive  acatzinco,  "the  little  reed  grass," 
the  letter  I  of  acatl  being  lost  in  composition. 

The  presence  of  undoubted  phonetic  elements  in  these  Aztec  glyphs 
expressing  personal  names  and  place  names  would  seem  to  indicate 
that  some  similar  usage  probably  prevailed  among  the  Maya. 

1  Thus  the  whole  rebus  in  figure  14  reads:  "Eye  bee  leaf  ant  rose  can  well  bear  awl  four  ewe."  These  words 
may  be  replaced  by  their  homophones  as  follows:  "I  believe  Aunt  Rose  can  well  bear  all  for  you." 

Rebus  writing  depends  on  the  principle  of  homophones;  that  is,  words  or  characters  which  sound  alike 
but  have  different  meanings. 


30 


BUEEAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


While  admitting  this  restricted  use  of  phonetic  composition  by  the 
Maya,  Professor  Seler  refuses  to  recognize  its  further  extension : 

Certainly  there  existed  in  the  Maya  writing  compound  hieroglyphs  giving  the  name 
of  a  deity,  person,  or  a  locality,  whose  elements  united  on  the  phonetic  principle. 
But  as  yet  it  is  not  proved  that  they  wrote  texts.  And  without  doubt  the  greater 
part  of  the  Maya  hieroglyphics  were  conventional  symbols  built  up  on  the  ideographic 
principle. 

Doctor  Forstemann  also  regards  the  use  of  phonetic  elements  as 
restricted  to  little  more  than  the  above  when  he  says,  '^Finally  the 
graphic  system  of  the  Maya  .  .  .  never  even  achieved  the  expres- 
sion of  a  phrase  or  even  a  verb." 

On  the  other  hand,  Mr.  Bowditch  (1910:  p.  255)  considers  the  use 
of  phonetic  composition  extended  considerably  beyond  these  limits : 

As  far  as  I  am  aware,  the  use  of  this  kind  of  writing  [rebus] 
was  confined,  among  the  Aztecs,  to  the  names  of  persons  and 
places,  while  the  Mayas,  if  they  used  the  rebus  form  at  all, 
used  it  also  for  expressing  common  nouns  and  possibly  ab- 
stract ideas.  The  Mayas  surely  used  picture  writing  and  the 
ideographic  system,  but  I  feel  confident  that  a  large  part  of 
Iheir  hieroglyphs  will  be  found  to  be  made  up  of  rebus  forms 
and  that  the  true  line  of  research  will  be  found  to  lie  in  this 

direction. 
I-IG.  15.   Aztec  place  names: 

a,  The  sign  for  the  town      Doctor  Bnntou  (1894  b:  p.  13)  held  an  opinion 
t^he"to^'Acat?4o!^  ^""^   l^ctwccn  these  two,  perhaps  inclining  slightly 
toward  the  former:  ''The  intermediate  position 
which  I  have  defended,  is  that  while  chiefly  ideographic,  they  [the 
Maya  glyphs]  are  occasionally  phonetic,  in  the  same  manner  as  are 
confessedly  the  Aztec  picture-writings." 

These  quotations  from  the  most  eminent  authorities  on  the  sub- 
ject well  illustrate  their  points  of  agreement  and  divergence.  All 
admit  the  existence  of  phonetic  elements  in  the  glyphs,  but  disagree 
as  to  their  extent.  And  here,  indeed,  is  the  crux  of  the  whole  phonetic 
question.  Just  how  extensively  do  phonetic  elements  enter  into  the 
composition  of  the  Maya  glyphs  ?  Without  attempting  to  dispose 
of  this  point  definitely  one  way  or  the  other,  the  author  may  say  that 
he  believes  that  as  the  decipherment  of  Maya  writing  progresses, 
more  and  more  phonetic  elements  will  be  identified,  though  the  idea 
conveyed  by  a  glyph  will  always  be  found  to  overshadow  its  phonetic 
value. 

The  various  theories  above  described  have  not  been  presented  for 
the  reader's  extended  consideration,  but  only  in  order  to  acquaint 
him  with  the  probable  nature  of  the  Maya  glyphs.  Success  in 
deciphering,  as  we  shall  see,  has  not  come  through  any  of  the  above 
mentioned  lines  of  research,  which  will  not  be  pursued  further  in  this 
work. 


MGRLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


81 


In  taking  up  the  question  of  the  meaning  of  Maya  writing,  it  must 
be  admitted  at  the  outset  that  in  so  f af  as  they  have  been  deciphered 
both  the  inscriptions  and  the  codices  have  been  found  to  deal  pri- 
marily, if  indeed  not  exclusively,  with  the  counting  of  time  in  some 
form  or  other.  Doctor  Forstemann,  the  first  successful  interpreter 
of  the  codices,  has  shown  that  these  writings  have  for  their  principal 
theme  the  passage  of  time  in  its  varying  relations  to  the  Maya  calen- 
dar, ritual,  and  astronomy.  They  deal  in  great  part  with  the  sacred 
year  of  260  days,  known  to  the  Aztec  also  under  the  name  of  the 
tonalamatl,  in  connection  with  which  various  ceremonies,  offerings, 
sacrifices,  and  domestic  occupations  are  set  forth.  Doctor  Forste- 
mann believed  that  this  260-day  period  was  employed  by  the  priests 
in  casting  horoscopes  and  foretelling  the  future  of  individuals, 
classes,  and  tribes,  as  well  as  in  predicting  coming  political  events  and 
natural  phenomena;  or  in  other  words,  that  in  so  far  as  the  260-day 
period  was  concerned,  the  codices  are  nothing  more  nor  less  than 
books  of  prophecy  and  divination. 

The  prophetic  character  of  some  of  these  native  books  at  least  is 
clearly  indicated  in  a  passage  from  Bishop  Landa's  Relacion  (p.  286). 
In  describing  a  festival  held  in  the  month  TJo,  the  Bishop  relates  that 
"the  most  learned  priest  opened  a  book,  in  which  he  examined  the 
omens  of  the  year,  which  he  announced  to  all  those  who  were  present." 
Other  early  Spanish  writers  state  that  these  books  contain  the  ancient 
prophecies  and  indicate  the  times  appointed  for  their  fulfillment. 

Doctor  Thomas  regarded  the  codices  as  religious  calendars,  or 
rituals  for  the  guidance  of  the  priests  in  the  celebration  of  feasts, 
ceremonies,  and  other  duties,  seemingly  a  natural  inference  from  the 
character  of  the  scenes  portrayed  in  connection  with  these  260-day 
periods. 

Another  very  important  function  of  the  codices  is  the  presentation 
of  astronomical  phenomena  and  calculations.  The  latter  had  for 
their  immediate  object  in  each  case  the  determination  of  the  lowest 
number  which  would  exactly  contain  all  the  .  numbers  of  a  certain 
group.  These  lov/est  numbers  are  in  fact  nothing  more  nor  less  than 
the  least  common  multiple  of  changing  combinations  of  numbers, 
each  one  of  which  represents  the  revolution  of  some  heavenly  body. 
In  addition  to  these  calculations  deities  are  assigned  to  the  several 
periods,  and  a  host  of  mythological  allusions  are  introduced,  the 
significance  of  most  of  which  is  now  lost. 

The  most  striking  proof  of  the  astronomical  character  of  the  codices 
is  to  be  seen  in  pages  46-50  of  the  Dresden  Manuscript.  Here,  to 
begin  with,  a  period  of  2,920  days  is  represented,  which  exactly  con- 
tains five  Venus  years  of  584  ^  days  each  (one  on  each  page)  as  well 
as  eight  solar  years  of  365  days  each.  Each  of  the  Venus  years  is 
divided  into  four  parts,  respectively,  236,  90,  250,  and  8  days.  The 


'  The  period  of  the  synodical  revolution  of  Venus  as  computed  to-day  is  583.920  days. 


32 


BUKEAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


first  and  third  of  these  constitute  the  periods  when  Venus  was  the 
morning  and  the  evening  star,  respectively,  and  the  second  and 
fourth,  the  periods  of  invisibihty  after  each  of  these  manifestations. 
This  Venus-solar  period  of  2,920  days  was  taken  as  the  basis  from 
which  the  number  37,960  was  formed.  This  contains  13  Venus-solar 
periods,  65  Venus-years,  104  solar  years,  and  146  tonalamatls ,  or 
sacred  years  of  260  days  each.  Finally,  the  last  number  (37,960) 
with  all  the  subdivisions  above  given  was  thrice  repeated,  so  that 
these  five  pages  of  the  manuscript  record  the  passage  of  113,880  days, 
or  312  solar  years. 

Agaia,  on  pages  51-58  of  the  same  manuscript,  405  revolutions  of 
the  moon  are  set  down;  and  so  accurate  are  the  calculations  involved 
that  although  they  cover  a  period  of  nearly  33  years  the  total  number 
of  days  recorded  (11,959)  is  only  89/100  of  a  day  less  than  the  true 
time  computed  by  the  best  modern  method  ^ — certainly  a  remarkable 
achievement  for  the  aboriginal  mind.  It  is  probable  that  the  revo- 
lutions of  the  planets  Jupiter,  Mars,  Mercury,  and  Saturn  are  similarly 
recorded  in  the  same  manuscript. 

Toward  the  end  of  the  Dresden  Codex  the  numbers  become  greater 
and  greater  until,  in  the  so-called  serpent  numbers,''  a  grand  total 
of  nearly  twelve  and  a  half  million  days  (about  thirty-four  thousand 
years)  is  recorded  again  and  again.  In  these  well-nigh  inconceivable 
periods  all  the  smaller  units  may  be  regarded  as  coming  at  last  to  a 
more  or  less  exact  close.  What  matter  a  few  score  years  one  way  or 
the  other  in  this  virtual  eternity?  Finally,  on  the  last  page  of  the 
manuscript,  is  depicted  the  Destruction  of  the  World  (see  pi.  3),  for 
which  these  highest  numbers  have  paved  the  way.  Here  we  see  the 
rain  serpent,  stretching  across  the  sky,  belching  forth  torrents  of 
water.  Great  streams  of  water  gush  from  the  sun  and  moon.  The 
old  goddess,  she  of  the  tiger  claws  and  forbidding  aspect,  the  malevo- 
lent patroness  of  floods  and  cloudbursts,  overturns  the  bowl  of  the 
heavenly  waters.  The  crossbones,  dread  emblem  of  death,  decorate 
her  skirt,  and  a  writhing  snake  crowns  her  head.  Below  with 
downward-pointed  spears,  symbolic  of  the  universal  destruction,  the 
black  god  stalks  abroad,  a  screeching  bird  raging  on  his  fearsome 
head.  Here,  indeed,  is  portrayed  with  graphic  touch  the  final  all- 
engulfing  cataclysm. 

According  to  the  early  writers,  in  addition  to  the  astronomic,  pro- 
phetic, and  ritualistic  material  above  described,  the  codices  con- 
tained records  of  historical  events.    It  is  doubtful  whether  this  is 

1  According  to  modem  calculations,  the  period  of  the  lunar  revolution  is  29.530588,  or  approximately 
29§  days.  For  405  revolutions  the  accumulated  error  would  be  .03X405=  12.15  days.  This  error  the  Maya 
obviated  by  using  29.5  in  some  calculations  and  29.6  in  others,  the  latter  offsetting  the  former.  Thus  the 
first  17  revolutions  of  the  sequence  are  divided  into  three  groups;  the  first  6  revolutions  being  computed 
at  29.5,  each  giving  a  total  of  177  days;  and  the  second  6  revolutions  also  being  computed  at  29.5  each, 
giving  a  total  of  another  177  days.  The  third  group  of  5  revolutions,  however,  was  computed  at  29.6  each, 
giving  a  total  of  148  days.  The  total  number  of  days  in  the  first  17  revolutions  was  thus  computed  to  be 
177+177+147=502,  which  is  very  close  to  the  time  computed  by  modern  calculations,  502.02. 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57    PLATE  3 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


33 


true  of  aay  of  the  three  codices  qow  extant,  though  there  are  grounds 
for  believing  that  the  Codex  Peresianus  may  be  in  part  at  least  of  an 
historical  nature. 

Much  less  progress  has  been  made  toward  discovering  the  meaning 
of  the  inscriptions.    Doctor  Brinton  (1894  b:  p.  32)  states: 

My  own  conviction  is  that  they  [the  inscriptions  and  codices]  will  prove  to  be 
much  more  astronomical  than  even  the  latter  [Doctor  Forstemaiin]  believes;  that 
they  are  primarily  and  essentially  records  of  the  motions  of  the  heavenly  bodies ;  and 
that  both  figures  and  characters  are  to  be  interpreted  as  referring  in  the  first  instance 
to  the  sun  and  moon,  the  planets,  and  those  constellations  which  are  most  prominent 
in  the  nightly  eky  in  the  latitude  of  Yucatan. 

Mr.  Bowditch  (1910:  p.  199)  has  also  brought  forward  very  cogent 
points  tending  to  show  that  in  part  at  least  the  inscriptions  treat  of  the 
intercalation  of  days  necessary  to  bring  the  dated  monuments,  based 
on  a  365-day  year,  into  harmony  with  the  true  solar  year  of  365.2421 
days.^ 

While  admitting  that  the  inscriptions  may,  and  probably  do, 
contain  such  astronomical  matter  as  Doctor  Brinton  and  Mr.  Bow- 
ditch  have  suggested,  the  writer  believes  nevertheless  that  funda- 
mentally they  are  historical;  that  the  monuments  upon  which  they 
are  presented  were  erected  and  inscribed  on  or  about  the  dates  they 
severally  record;  and  finally,  that  the  great  majority  of  these  dates 
are  those  of  contemporaneous  events,  and  as  such  pertain  to  the 
subject-matter  of  history. 

The  reasons  which  have  led  him  to  this  conclusion  follow: 

First.  The  monuments  at  most  of  the  southern  Maya  sites  show 
a  certain  periodicity  in  their  sequence.  This  is  most  pronounced  at 
Quirigua,  where  all  of  the  large  monuments  fall  into  an  orderly 
series,  in  which  each  monument  is  dated  exactly  1,800  days  later  than 
the  one  imiriediately  preceding  it  in  the  sequence.  This  is  also  true 
at  Copan,  where,  in  spite  of  the  fact  that  there  are  many  gaps  in  the 
sequence,  enough  monuments  conforming  to  the  plan  remain  to 
prove  its  former  existence.  The  same  may  be  said  also  of  Naranjo, 
Seibal,  and  Piedras  Negras,  and  in  fact  of  almost  all  the  other  large 
cities  which  afford  sufficient  material  for  a  chronological  arrangement. 

This  interval  of  1,800  days  quite  obviously  was  not  determined  by 
the  recurrence  of  any  natural  phenomenon .  It  has  no  parallel  in 
nature,  but  is,  on  the  contrary,  a  highly  artificial  unit.  Consequently, 
monuments  the  erection  of  which  was  regulated  by  the  successive 
returns  of  this  period  could  not  depend  in  the  least  for  the  fact  of 
their  existence  on  any  astronomical  phenomenon  other  than  that  of 
the  rising  and  setting  of  eighteen  hundred  successive  suns,  an  arbi- 
trary period. 

The  Maya  of  Yucatan  had  a  similar  method  of  marking  time, 
though  their  unit  of  enumeration  was  7,200  days,  or  four  times  the 


1  This  is  the  tropical  year  or  the  time  from  one  equinox  to  its  return. 
43508°— Bull.  57—15  3 


34 


BUKEAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


length  of  the  one  used  for  the  same  purpose  in  the  older  cities.  The 
following  quotations  from  early  Spanish  chroniclers  explain  this 
practice  and  indicate  that  the  inscriptions  presented  on  these  time- 
markers  were  of  an  historical  nature  : 

There  were  discovered  in  the  plaza  of  that  city  [Mayapan]  seven  or  eight  stones 
each  ten  feet  in  length ,  round  at  the  end,  and  well  worked.  These  had  some  writings 
in  the  characters  which  they  use,  but  were  so  worn  by  water  that  they  could  not  be 
read.  Moreover,  they  think  them  to  be  in  memory  of  the  foundation  and  destruction 
of  that  city.  There  are  other  similar  ones,  although  higher,  at  Zilan,  one  of  the  coast 
towns.  The  natives  when  asked  what  these  things  were,  replied  that  they  were 
accustomed  to  erect  one  of  these  stones  every  twenty  years,  which  is  the  number 
they  use  for  counting  their  ages.^ 

The  other  is  even  more  explicit: 

Their  lustras  having  reached  five  in  number,  which  made  twenty  years,  which 
they  call  a  katun,  they  place  a  graven  stone  on  another  of  the  same  kind  laid  in  lime 
and  sand  in  the  walls  of  their  temples  and  the  houses  of  the  priests,  as  one  still  sees 
to-day  in  the  edifices  in  question,  and  in  some  ancient  walls  of  our  own  convent  at 
Merida,  about  which  there  are  some  cells.  In  a  city  named  Tixhualatun,  which  sig- 
nifies "place  where  one  graven  stone  is  placed  upon  another,"  they  say  are  their 
archives,  where  everybody  had  recourse  for  events  of  all  kinds,  as  we  do  to 
Simancas.2 

It  seems  almost  necessary  to  conclude  from  such  a  parallel  that 
the  inscriptions  of  the  southern  cities  will  also  be  found  to  treat  of 
historical  matters. 

Second,  When  the  monuments  of  the  southern  cities  are  arranged 
according  to  their  art  development,  that  is,  in  stylistic  sequence,  they 
are  found  to  be  arranged  in  their  chrtDnological  order  as  well.  This 
important  discovery,  due  largely  to  the  researches  of  Dr.  H.  J. 
Spinden,  has  enabled  us  to  determine  the  relative  ages  of  various 
monuments  quite  independent  of  their  respective  dates.  From  a 
stylistic  consideration  alone  it  has  been  possible  not  only  to  show 
that  the  monuments  date  from  different  periods,  but  also  to  establish 
the  sequence  of  these  periods  and  that  of  the  monuments  in  them. 
Finally,  it  has  demonstrated  beyond  all  doubt  that  the  great 
majority  of  the  dates  on  Maya  monuments  refer  to  the  time  of  their 
erection,  so  that  the  inscriptions  which  they  present  are  historical  in 
that  they  are  the  contemporaneous  records  of  different  epochs. 

TJiird.  The  dates  on  the  monuments  are  such  as  to  constitute  a 
strong  antecedent  probability  of  their  historical  character.  Like 
the  records  of  most  ancient  peoples,  the  Maya  monuments,  judging 
from  their  dates,  were  at  first  scattered  and  few.  Later,  as  new 
cities  were  founded  and  the  nation  waxed  stronger  and  stronger,  the 
number  of  monuments  increased,  until  at  the  flood  tide  of  Maya  pros- 
perity they  were,  comparatively  speaking,  common.  Finally,  as 
decline  set  in,  fewer  and  fewer  monuments  were  erected,  and  eventu- 
ally effort  in  this  field  ceased  altogether.    The  increasing  number  of 


1  Landa,  1864:  p.  52, 


2Cogolludo,  1688:  i,  lib.  iv,  v,  p.  186. 


•0  "0  '0  "OT" 
•0  -01  -61  -6  ■ 
•0  -0   •61  "6  " 

•0  -OT  •81  •e  ■ 

•0  •O   •81  '&  " 

•0  •OT  'II  -6  ■ 

•0  •O  '11  '6  ■ 

•0  -OT  '91  '6  ■ 

•0  -0  '91  •e  ■ 

•0  -OT  -51  -6  ■ 
•0  •O  '91  -6  • 

•0  •OX  -fi  •e  ■ 

•0  '0  "^l  "6  ■ 

•0  -01  •81  •e  ■ 

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•0  -OT  'Zl  '6  ■ 

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•0  "01  •OT  '6  • 

•0  -0  -01  •e  • 
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•0  -0  '6  '6  ' 

•0  '01  "8  '6 

•0  •O  '8  '6  ' 

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■0  -0  'L  '6 

•0  •OI  •g  •e 

•0  •Q  '9  '6 

•0  '01  '9  '6 

•0  -0  '9  '6 

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•0  •OI  •g  '6 

•0*0  '8  "6 

•0  •OI  -z  •e 

•0^0  'Z  -6 


MORLEY]      INTEODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  35 

the  monuments  by  ten-year  periods  is  shown  in  plate  4,  where  the* 
passage  of  time  (i.  e.,  the  successive  ten-year  periods)  is  represented 
from  left  to  right,  and  the  number  of  dates  in  each  ten-year  period 
from  bottom  to  top.  Although  other  dated  monuments  will  be 
found  from  time  to  time,  which  will  necessarily  change  the  details 
given  in  this  diagram,  such  additional  evidence  in  all  probability  will 
never  controvert  the  following  general  conclusions,  embodied  in  what 
has  just  been  stated,  which  are  deducible  from  it: 

1.  At  first  there  was  a  long  period  of  slow  growth  represented  by 
few  monuments,  which,  however,  increased  in  number  toward  the  end. 

2.  This  was  followed  without  interruption  by  a  period  of  increased 
activity,  the  period  from  which  the  great  majority  of  the  monuments 
date. 

3.  Finally  this  period  came  to  rather  an  abrupt  end,  indicated  by 
the  sudden  cessation  in  the  erection  of  dated  monuments. 

The  consideration  of  these  indisputable  facts  tends  to  establish  the 
historical  rather  than  the  astronomical  character  of  the  monuments. 
For  had  the  erection  of  the  monuments  depended  on  the  successive 
recurrences  of  some  astronomical  phenomenon,  there  would  be  cor- 
responding intervals  between  the  dates  of  such  monuments  ^  the 
length  of  which  would  indicate  the  identity  of  the  determining  phe- 
nomenon; and  they  would  hardly  have  presented  the  same  logical 
increase  due  to  the  natural  growth  of  a  nation,  which  the  accompany- 
ing diagram  clearly  sets  forth. 

Fourth.  Although  no  historical  codices  ^  are  known  to  have  sur- 
vived, history  was  undoubtedly  recorded  in  these  ancient  Maya 
books.  The  statements  of  the  early  Spanish  writers  are  very  expUcit 
on  this  point,  as  the  following  quotations  from  their  works  will  show. 
Bishop  Landa  (here,  as  always,  one  of  the  most  rehable  authori- 
ties) says:  ''And  the  sciences  which  they  [the  priests]  taught  were 
the  count  of  the  years,  months  and  days,  the  feasts  and  ceremonies, 
the  administration  of  their  sacraments,  days,  and  fatal  times,  their 
methods  of  divination  and  prophecy,  and  foretelling  events,  and  the 
remedies  for  the  sick,  and  their  antiquities"  [p.  44].  And  again,  "  they 
[the  priests]  attended  the  service  of  the  temples  and  to  the  teaching 
of  their  sciences  and  how  to  write  them  in  their  hoolcs.''  And  again, 
[p.  316],  ''This  people  also  used  certain  characters  or  letters  with 
which  they  wrote  in  their  hoolcs  their  ancient  matters  and  sciences." 

Father  Lizana  says  (see  Landa,  1864:  p.  352):  "The  history  and 
authorities  we  can  cite  are  certain  ancient  characters,  scarcely  under- 
stood by  many  and  explained  by  some  old  Indians,  sons  of  the  priests 

1  For  example,  if  the  revolution  of  Venus  had  been  the  governing  phenomenon,  each  monument  would 
be  distant  from  some  other  by  584  days;  if  that  of  Mars,  780  days;  if  that  of  Mercury,  115  or  116  days,  etc. 
Furthermore,  the  sequence,  once  commenced,  would  naturally  have  been  more  or  less  uninterrupted.  It 
is  hardly  necessary  to  repeat  that  the  intervals  which  have  been  found,  namely,  7200  and  1800,  rest  on  no 
known  astronomical  phenomena  but  are  the  direct  result  of  the  Maya  vigesimal  system  of  numeration. 

2  It  is  possible  that  the  Codex  Peresianus  may  treat  of  historical  matter,  as  already  explained. 


36 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


of  their  gods,  who  alone  knew  how  to  read  and  expound  them  and 
who  were  beheved  in  and  revered  as  much  as  the  gods  themselves." 

Father  Ponce  (tome  lviii,  p.  392)  who  visited  Yucatan  as  early  as 
1588,  is  equally  clear:  "The  natives  of  Yucatan  are  among  all  the 
inhabitants  of  New  Spain  especially  deserving  of  praise  for  three 
things.  First  that  before  the  Spaniards  came  they  made  use  of 
characters  and  letters  with  which  they  wrote  out  tJieir  Mstories,  their 
ceremonies,  the  order  of  sacrifices  to  their  idols  and  their  calendars 
in  books  made  of  the  bark  of  a  certain  tree." 

Doctor  Aguilar,  who  wrote  but  little  later  (1596),  gives  more  details 
as  to  the  kind  of  events  which  were  recorded.  "On  these  [the  fiber 
books]  they  painted  in  color  the  reckoning  of  their  years,  wars,  pesti- 
lences, hurricanes,  inundations,  famines  and  other  events." 

Finally,  as  late  as  1697,  some  of  these  historical  codices  were  in  the 
possession  of  the  last  great  independent  Maya  rider,  one  Canek. 
Says  Villagutierre  (1701:  lib.  vi,  cap.  iv)  in  this  connection:  "Because 
their  king  [Canek]  had  read  it  in  his  analtehes  [fiber-books  or  codices] 
they  had  knowledge  of  the  provinces  of  Yucatan,  and  of  the  fact  that 
their  ancestors  had  formerly  come  from  them;  analtehes  or  histories 
being  one  and  the  same  thing." 

It  is  clear  from  the  foregoing  extracts,  that  the  Maya  of  Yucatan 
recorded  their  history  up  to  the  time  of  the  Spanish  Conquest,  in  their 
hieroglyphic  books,  or  codices.  That  fact  is  beyond  dispute.  It 
must  be  remembered  also  in  this  connection,  that  the  Maya  of  Yucatan 
were  the  direct  inheritors  of  that  older  Maya  civilization  in  the  south, 
which  had  produced  the  hieroglyphic  monuments.  For  this  latter 
reason  the  writer  believes  that  the  practice  of  recording  history  in  the 
hieroglyphic  writing  had  its  origin,  along  with  many  another  custom, 
in  the  southern  area,  and  consequently  that  the  inscriptions  on  the 
monuments  of  the  southern  cities  are  probably,  in  part  at  least,  of  an 
historical  nature. 

Whatever  may  be  the  meaning  of  the  undeciphered  glyphs,  enough 
has  been  said  in  this  chapter  about  those  of  known  meaning  to  indi- 
cate the  extreme  importance  of  the  element  of  time  in  Maya  writing. 
The  very  great  preponderance  of  astronomical,  calendary,  and  nu- 
merical signs  in  both  the  codices  and  the  inscriptions  has  determined, 
so  far  as  the  beginner  is  concerned,  the  best  way  to  approach  the 
study  of  the  glyphs.  First,  it  is  essential  to  understand  thoroughly 
the  Maya  system  of  counting  time,  in  other  words,  their  calendar  and 
chronology.  Second,  in  order  to  make  use  of  this  knowledge,  as  did 
the  Maya,  it  is  necessary  to  f  amiharize  ourselves  with  their  arithmetic 
and  its  signs  and  symbols.  Third,  and  last,  after  this  has  been 
accomplished,  we  are  ready  to  apply  ourselves  to  the  deciphering 
of  the  inscriptions  and  the  codices.  For  this  reason  the  next  chapter 
will  be  devoted  to  the  discussion  of  the  Maya  system  of  counting  time. 


Chapter  III.    HOW  THE  ]\IAYA  RECKONED  TIME 


Among^all  peoples  and  in  all  ages  the  most  obvious  vmit  for  the 
measurement  of  time  has  been  the  day;  and  the  never-failing  reap- 
pearance of  light  after  each  interval  of  darkness  has  been  the  most 
constant  natural  phenomenon  with  which  the  mind  of  man  has  had 
to  deal.  From  the  earliest  times  successive  returns  of  the  siin  have 
regulated  the  whole  scheme  of  human  existence.  When  it  was  light, 
man  worked;  when  it  was  dark,  he  rested.  Conformity  to  the  opera- 
tion of  this  natural  law  has  been  practically  imiversal. 

Indeed,  as  primitive  man  saw  nature,  day  was  the  only  division  of 
time  upon  which  he  could  absolutely  rely.  The  waxing  and  waning 
of  the  moon,  with  its  everchanging  shape  and  occasional  obscuration 
by  clouds,  as  well  as  its  periodic  disappearances  from  the  heavens 
all  combined  to  render  that  luminary  of  little  account  in  measuring 
the  passage  of  time.  The  round  of  the  seasons  was  even  more  unsat- 
isfactory. A  late  spring  or  an  early  winter  by  hastening  or  retarding 
the  return  of  a  season  caused  the  apparent  lengths  of  succeeding 
years  to  vary  greatly.  Even  where  a  365-day  year  had  been  deter- 
mined, the  fractional  loss,  amounting  to  a  day  every  four  years,  soon 
brought  about  a  discrepancy  between  the  calendar  and  the  true  year. 
The  day,  therefore,  as  the  most  obvious  period  in  nature,  as  well  as 
the  most  reliable,  has  been  used  the  world  over  as  the  fundamental 
unit  for  the  measurement  of  longer  stretches  of  time. 

'  Table  I.    THE  TWENTY  MAYA  DAY  NAMES 


Imix 

Chuen 

Ik 

Eb 

Akbal 

Ben 

Kan 

Ix 

Chicchan 

Men 

Cimi 

Cib 

Manik 

Caban 

Lamat 

Eznab 

Muluc 

Cauac 

Oc 

Ahau 

In  conformity  with  the  universal  practice  just  mentioned  the  Maya 
made  the  day,  which  they  called  Icin,  the  primary  unit  of  their  calen- 
dar. There  were  twenty  such  units,  named  as  in  Table  I;  these 
followed  each  other  in  the  order  there  shown.  When  Ahau,  the  last 
day  in  the  list,  had  been  reached,  the  count  began  anew  with  Imix, 
and  thus  repeated  itself  again  and  again  without  interruption, 
throughout  tune.    It  is  important  that  the  student  should  fix  this 

37 


38 


BUEEAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


Maya  conception  of  the  rotation  of  days  firmly  in  his  mind  at  the 
outset,  since  all  that  is  to  follow  depends  upon  the  absolute  con- 
tinuity of  this  twenty-day  sequence  in  endless  repetition. 


MIX 


9 

CHICCHAN 


CIMI 


0 

MANIK 


LA  MAT 


Fig.  16.   The  day  signs  in  the  inscriptions. 


The  glyphs  for  these  twenty  days  are  shown  in  figures  16  and  17. 
The  forms  in  figure  16  are  from  the  inscriptions  and  those  in  figure 
17  from  the  codices.  In  several  cases  variants  are  given  to  facilitate 
identification.  A  study  of  the  glyphs  in  these  two  figures  shows  on 
the  whole  a  fairly  close  similarity  between  the  forms  for  the  same 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


39 


day  in  each.  The  sign  for  the  first  day,  Imix,  is  practically  identical 
in  both.  Compare  figure  16,  a  and  I,  with  figure  17,  a  and  h.  The 
usual  form  for  the  day  Ik  m  the  inscriptions  (see  fig.  16,  c),  however, 


CKUEN  EB  BEN  IX 


a'  y  C  d' 

EZNAB  CAUAC  AHAU 


Fig.  17.   The  day  signs  in  the  codices. 

is  unlike  the  glyph  for  the  same  day  in  the  codices  (fig.  17,  c,  d) . 
The  forms  for  Akbal  and  Kan  are  practically  the  same  in  each  (see  fig. 
16,  d,  e,  and/,  and  fig.  17,  e  and/,  respectively) .  The  day  Chicchan, 
figure  16,  g,  occurs  rarely  in  the  inscriptions;  when  present,  it  takes  the 


40 


BUKEAU  OF  AMERICAN  ETHNOLOGY 


fBULL.  57 


form  of  a  grotesque  head.  In  the  codices  the  common  form  for  this 
day  is  very  different  (fig.  17,  g) .  The  head  variant,  however  (fig. 
17,  li) ,  shows  a  slightly  closer  similarity  to  the  form  from  the  inscrip- 
tions. The  forms  in  both  figure  16,  Ji,  i,  and  figure  17,  i,  j,  for  the 
day  Cimi  show  little  resemblance  to  each  other.  Although  figure  17, 
i,  represents  the  common  form  in  the  codices,  the  variant  in  j  more 
closely  resembles  the  form  in  figure  16,  h,  i.  The  day  Manik  is  prac- 
tically the  same  in  both  (see  figs.  16,  j,  and  17,  ^),  as  is  also  lamat 
(figs.  16,  Ic,  Z,  and  17,  Z,  m).  The  day  Muluc  occurs  rarely  in  the 
inscriptions  (fig.  16,  m,  n) .  Of  these  two  variants  m  more  closely 
resembles  the  form  from  the  codices  (fig.  17,  n) .  The  glyph  for  the 
day  Oc  (fig.  16,  o,  jp,  q)  is  not  often  found  in  the  inscriptions.  In  the 
codices,  on  the  other  hand,  this  day  is  frequently  represented  as 
shown  in  figure  17,  o.  This  form  bears  no  resemblance  to  the  forms 
in  the  inscriptions.  There  is,  however,  a  head-variant  form  found 
very  rarely  in  the  codices  that  bears  a  slight  resemblance  to  the  forms 
in  the  inscriptions.  The  day  Chuen  occurs  but  once  in  the  inscrip- 
tions where  the  form  is  clear  enough  to  distinguish  its  characteristic 
(see  fig  16,  r) .  This  form  bears  a  general  resemblance  to  the  glyph 
for  this  day  in  the  codices  (fig.  17,  p,  q).  The  forms  for  the  day  Eb 
in  both  figures  16,  s,  t,  u,  and  17,  r,  are  grotesque  heads  showing 
but  remote  resemblance  to  one  another.  The  essential  element  in 
both,  however,  is  the  same,  that  is,  the  element  occupying  the 
position  of  the  ear.  Although  the  day  Ben  occurs  but  rarely  in 
the  inscriptions,  its  form  (fig.  16,  v)  is  practically  identical  with 
that  in  the  codices  (see  fig.  17,  s).  The  day  Ix  in  the  inscriptions 
appears  as  in  figure  16,  w,  x.  The  form  in  the  codices  is  shown  in 
figure  17,  ^.  The  essential  element  in  each  seems  to  be  the  three  promi- 
nent dots  or  circles.  The  day  Men  occurs  very  rarely  on  the  monu- 
ments. The  form  sho^\TL  in  figure  16,  is  a  grotesque  head  not  unlike 
the  sign  for  this  day  in  the  codices  (fig.  17,  u).  The  signs  for  the 
day  Cib  in  the  inscriptions  and  the  codices  (figs.  16,  z,  and  17,  v,  w), 
respectively,  are  very  dissimilar.  Indeed,  the  form  for  Cib  (fig.  17,  v) 
in  the  codices  resembles  more  closely  the  sign  for  the  day  Caban 
(fig.  16,  a',  h')  than  it  does  the  form  for  Cib  in  the  inscriptions  (see 
fig.  16,  z) .  The  only  element  common  to  both  is  the  line  paralleling  the 
upper  part  of  the  glyph  (*)  and  the  short  vertical  lines  connecting 
*  it  with  the  outline  at  the  top.  The  glyphs  for  the  day  Caban  in 
both  figures  16,  a',  V,  and  17,  x,  show  a  satisfactory  resemblance  to 
each  other.  The  forms  for  the  day  Eznab  are  also  practically  iden- 
tical (see  figs.  16,  c\  and  17,  z,  a') .  The  forms  for  the  day  Cauac,  on 
the  other  hand,  are  very  dissimilar;  compare  figures  16,  d\  and  17, 
The  only  point  of  resemblance  between  the  two  seems  to  be  the 
element  which  appears  in  the  eye  of  the  former  and  at  the  lower  left- 
hand  side  of  the  latter.    The  last  of  the  twenty  Maya  days,  and  by 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  41 

far  the  most  important,  since  it  is  found  in  both  the  codices  and  the 
inscriptions  more  frequently  than  all  of  the  others  combined,  is  Ahau 
(see  figs.  16,  e'-¥,  and  17,  c' ,  d') .  The  latter  form  is  the  only  one 
found  in  the  codices,  and  is  identical  with  e' ,  f,  figure  16,  the  usual 
sign  for  this  day  in  the  inscriptions.  The  variants  in  figure  16,  g'-V , 
appear  on  some  of  the  monuments,  and  because  of  the  great  im- 
portance of  this  day  Ahau  it  is  necessary  to  keep  all  of  them  in 
mind. 

These  examples  of  the  glyphs,  which  stand  for  the  twenty  Maya 
days,  are  in  each  case  as  typical  as  possible.  The  student  must 
remember,  however,  that  many  variations  occur,  which  often  render 
the  correct  identification  of  a  form  difficult.  As  explained  in  the 
preceding  chapter,  such  variations  are  due  not  only  to  individual 
peculiarities  of  style,  careless  drawing,  and  actual  error,  but  also  to 
the  physical  dissimilarities  of  materials  on  which  they  are  por- 
trayed, as  the  stone  of  the  monuments  and  the  fiber  paper  of  the 
codices;  consequently,  such  differences  may  be  regarded  as  unessen- 
tial. The  ability  to  identify  variants  differing  from  those  shown  in 
figures  16  and  17  will  come  only  through  experience  and  familiarity 
with  the  glyphs  themselves.  The  student  should  constantly  bear  in 
mind,  however,  that  almost  every  Maya  glyph,  the  signs  for  the  days 
included,  has  an  essential  element  peculiar  to  it,  and  the  discovery  of 
such  elements  will  greatly  facilitate  his  study  of  Maya  writing. 

Why  the  named  days  should  have  been  limited  to  twenty  is  diffi- 
cult to  understand,  as  this  number  has  no  parallel  period  in  nature. 
Some  have  conjectured  that  this  number  was  chosen  because  it  rep- 
resents the^  number  of  man's  digits,  the  twenty  fingers  and  toes. 
Mr.  Bowditch  has  pointed  out  in  this  connection  that  the  Maya  word 
for  the  period  composed  of  these  twenty  named  days  is  uinal,  while  the 
word  for  ^man'  is  uinik.  The  parallel  is  interesting  and  may  possibly 
explain  why  the  number  twenty  was  selected  as  the  basis  of  the 
Maya  system  of  numeration,  which,  as  we  shall  see  later,  was  vigesi- 
mal, that  is,  increasing  by  twenties  or  multiples  thereof. 

The  Tonalamatl,  or  260-day  Period 

Merely  calling  a  day  by  one  of  the  twenty  names  given  in  Table  I, 
however,  did  not  sufficiently  describe  it  according  to  the  Maya  notion. 
For  instance,  there  was  no  day  in  the  Maya  calendar  called  merely 
Imix,  Ik,  or  Akbal,  or,  in  fact,  by  any  of  the  other  names  given  in 
Table  I.  Before  the  name  of  a  day  was  complete  it  was  necessary 
to  prefix  to  it  a  number  ranging  from  1  to  13,  inclusive,  as  6  Imix 
or  13  Akbal.  Then  and  only  then  did  a  Maya  day  receive  its  com- 
plete designation  and  find  its  proper  place  in  the  calendar. 

The  manner  in  which  these  thirteen  numbers,  1  to  13,  inclusive, 
were  joined  to  the  twenty  names  of  Table  I  was  as  follows:  Selecting 


42 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


any  one  of  the  twenty  names  ^  as  a  starting  point,  Kan  for  example, 
the  number  1  was  prefixed  to  it.  See  Table  II,  in  which  the  names 
of  Table  I  have  been  repeated  with  the  numbers  prefixed  to  them  in 
a  manner  to  be  explained  hereafter.  The  star  opposite  the  name 
Kan  indicates  the  starting  point  above  chosen.  The  name  Chicclian 
immediately  following  Kan  in  Table  II  was  given  the  next  number 
in  order  (2),  namely,  2  Chicchan.  The  next  name,  Cimi,  was  given 
the  next  number  (3),  namely,  3  Cimi,  and  so  on  as  follows:  4  Manik, 
5  Lamat,  6  Muluc,  7  Oc,  8  Chuen,  9  Eb,  10  Ben,  11  Ix,  12  Men,  13  Cib. 


Instead  of  giving  to  the  next  name  in  Table  II  (Caban)  the 
number  14,  the  number  1  was  prefixed;  for,  as  previously  stated, 
the  numerical  coefficients  of  the  days  did  not  rise  above  the  num- 
ber 13.  Follo^ving  the  day  1  Caban,  the  sequence  continued  as 
before:  2  Eznab,  3  Cauac,  4  Ahau.  After  the  day  4  Ahau,  the  last 
in  Table  II,  the  next  number  in  order,  in  this  case  5,  was  prefixed  to 
the  next  name  in  order — that  is,  Imix,  the  first  name  in  Table  II — 
and  the  count  continued  mthout  interruption:  6  Imix,  6  Ik,  7  Akbal, 
or  back  to  the  name  Kan  with  which  it  started.  There  was  no  break 
in  the  sequence,  however,  even  at  this  point  (or  at  any  other,  for 
that  matter) .  The  next  name  in  Table  II,  Kan,  selected  for  the 
starting  point,  was  given  the  number  next  in  order,  i.  e.,  8,  and  the 
day  following  7  Akbal  in  Table  II  would  be,  therefore,  8  Kan,  and 
the  sequence  would  continue  to  be  formed  in  the  same  way:  8 
Kan,  9  Chiccban,  10  Cimi,  11  Manik,  12  Lamat,  13  Muluc,  1  Oc, 
2  Cbuen,  3  Eb,  and  so  on.  So  far  as  the  Maya  conception  of  time  was 
concerned,  this  sequence  of  days  went  on  without  interruption,  forever. 

While  somewhat  unusual  at  first  sight,  this  sequence  is  in  reality 
exceedingly  simple,  being  governed  by  three  easily  remembered  rules : 

Rule  1 .  The  sequence  of  the  20  day  names  repeats  itself  again  and 
again  without  interruption. 

1  Since  the  sequence  of  the  twenty  day  names  was  continuous,  it  is  obvious  that  it  had  no  beginning  or  end- 
ing, like  the  rim  of  a  wheel;  consequently  any  day  name  may  be  chosen  arbitrarily  as  the  starting  point.  In 
the  accompanying  example  Kan  has  been  chosen  to  begin  with,  though  Bishop  Landa  (p.  236)  states 
with  regard  to  the  Maya:  "The  character  or  letter  with  which  they  commence  their  count  of  the 
^Jjj)  days  or  calendar  is  called  Hun-ymix  fi.  e.  1  Imix]".   Again,  "Here  commences  the  count  of  the  cal- 

*     endar  of  the  Indians,  saying  in  their  language  Hun  Imix  (*)  [i.  e.  1  Imix]."   (Ibid.,  p.  246.) 


Table  II.  SEQUENCE  OF  MAYA  DAYS 


5  Imix 

6  Ik 

7  Akbal 
*1  Kan 

2  Chicclian 

3  Cimi 

4  Manik 

5  Lamat 

6  Muluc 

7  Oc 


8  Chuen 

9  Eb 

10  Ben 

11  Ix 

12  Men 

13  Cib 

1  Caban 

2  Eznab 

3  Cauac 

4  Ahau 


BUREAU  OF  AMERICAN  ETHNOLOGY 


S.O  Cimi  (c; 
Chicchan  (s; 
Kan  w 
Akbal  (3) 
Ik 

\  Imix 


(2) 

^58) 


TONALAMATL  WHEEL,   SHOWING  SEQUEN( 


BULLETIN  57    PLATE  5 


1^ 


Oft 

u9nq 


<i3  2 
u&a 


6^ 


^  ^  « ^  -  2  «>  ^r^S'V^ 


OF  THE  260   DIFFERENTLY   NAMED  DAYS 


\ 


MORLEY]       INTRODUCTIOlSr  TO  STUDY  OF  MAYA  HIEROGLYPHS 


48 


Rule  2.  The  sequence  of  the  numerical  coefficients  1  to  13,  inclusive, 
repeats  itself  again  and  again  without  interruption,  1  following  im- 
mediately 13. 

Rule  3.  The  13  numerical  coefficients  are  attached  to  the  20  names, 
so  that  after  a  start  has  been  made  by  prefixing  any  one  of  the  13 
numbers  to  any  one  of  the  20  names,  the  number  next  in  order  is 
given  to  the  name  next  in  order,  and  the  sequence  continues  indefi- 
nitely in  this  manner. 

It  is  a  simple  question  of  arithmetic  to  determine  the  number  of 
days  which  must  elapse  before  a  day  bearing  the  same  designation 
as  a  previous  one  in  the  sequence  can  reappear.  Since  there  are 
13  numbers  and  20  names,  and  since  each  of  the  13  numbers  must 
be  attached  in  turn  to  each  one  of  the  20  names  before  a  given  number 
can  return  to  a  given  name,  we  must  find  the  least  common  multiple 
of  13  and  20.  As  these  two  numbers,  contain  no  common  factor, 
their  least  common  multiple  is  their  product  (260),  which  is  the  num- 
ber sought.  Therefore,  any  given  day  can  not  reappear  in  the  se- 
quence until  after  the  259  days  immediately  following  it  shall  have 
elapsed.  Or,  in  other  words,  the  261st  day  will  have  the  same 
designation  as  the  1st,  the  262d  the  same  as  the  2d,  and  so  on. 

This  is  graphically  shown  in  the  wheel  figured  in  plate  5,  where  the 
sequence  of  the  days,  commencing  with  1  Imix,  which  is  indicated 
by  a  star,  is  represented  as  extending  around  the  rim  of  the  wheel. 
After  the  name  of  each  day,  its  number  in  the  sequence  beginning  with 
the  starting  point  1  Imix,  is  shown  in  parenthesis.  Now,  if  the  star 
opposite  the  day  1  Imix  be  conceived  to  be  stationary  and  the  wheel 
to  revolve  in  a  sinistral  circuit,  that  is  contra-clockwise,  the  days  will 
pass  the  stardn  the  order  which  they  occupy  in  the  260-day  sequence. 
It  appears  from  this  diagram  also  that  the  day  1  Imix  can  not  recur 
until  after  260  days  shall  have  passed,  and  that  it  always  follows  the 
day  13  Ahau.  This  must  be  true  since  Aliau  is  the  name  immediately 
preceding  Imix  in  the  sequence  of  the  day  names  and  13  is  the  number 
immediately  preceding  1.  After  the  day  13  Ahau  (the  260th  from 
the  starting  point)  is  reached,  the  day  1  Imix,  the  261st,  recurs  and 
the  sequence,  having  entered  into  itself  again,  begins  anew  as  before. 

This  round  of  the  260  differently  named  days  was  called  by  the 
Aztec  the  tonalamatl,  or  ^'book  of  days.''  The  Maya  name  for  this 
period  is  unknown  ^  and  students  have  accepted  the  Aztec  name  for 
it.  The  tonalamatl  is  frequently  represented  in  the  Maya  codices, 
there  being  more  than  200  examples  in  the  Codex  Tro-Cortesiano 
alone.  It  was  a  very  useful  period  for  the  calculations  of  the  priests 
because  of  the  different  sets  of  factors  into  which  it  can  be  resolved, 


1  Professor  Seler  says  the  Maya  of  Guatemala  called  this  period  the  Jcin  katun,  or  "order  of  the  days." 
He  fails  to  give  his  authority  for  this  statement,  however^  and,  as  will  appear  later,  these  terms  have 
entirely  different  meanings.   (See  Bulletin  28,  p.  14.) 


44 


BUREAU  OF  AMEEICAN  ETHNOLOGY 


[bull.  5? 


namely,  4x65,  5X52,  10X26,  13X20,  and  2X130.  Tonalamatls 
divided  into  4,  5,  and  10  equal  parts  of  65,  52,  and  26  days,  respec- 
tively, occur  repeatedly  throughout  the  codices. 

It  is  all  the  more  curious,  therefore,  that  this  period  is  rarely 
represented  in  the  inscriptions.   The  writer  recalls  but  one  city  (Copan) 
in  which  this  period  is  recorded  to  any  considerable  extent. 
It  might  almost  be  inferred  from  this  fact  alone  that  the 
inscriptions  do  not  treat  of  prophecy,  divinations,  or  ritu- 
alistic and  ceremonial  matters,  since  these  subjects  in  the 
codices  are  always  found  in  connection  with  tonalamatls. 
If  true  this  considerably  restricts  the  field  of  which  the 
inscriptions  may  treat. 
Fig.  18.  Sign      Mr.  Goodmau  has  identified  the  glyph  shown  in  figure 
matf ^(accord-  18  as  the  sigu  for  the  260-day  period,  but  on  wholly  insuffi- 
ing  to  Good-  cicut  cvidcnce  the  writer  believes.    On  the  other  hand,  so 
important  a  period  as  the  tonalamatl  undoubtedly  had 
its  own  particular  glyph,  but  up  to  the  present  time  all  efforts  to 
identify  this  sign  have  proved  unsuccessful. 

The  Haab,  or  Year  of  365  Days 

Having  explained  the  composition  and  nature  of  the  tonalamatl, 
or  so-called  Sacred  Year,  let  us  turn  to  the  consideration  of  the  Solar 
Year,  which  was  known  as  liaah  in  the  Maya  language. 

The  Maya  used  in  their  calendar  system  a  365-day  year,  though 
they  doubtless  knew  that  the  true  length  of  the  year  exceeds  this 
by  6  hours.  Indeed,  Bishop  Landa  very  explicitly  states  that  such 
knowledge  was  current  among  them.  ''They  had,"  he  says,  'Hheir 
perfect  year,  like  ours,  of  365  days  and  6  hours;"  and  again,  ''The 
entire  year  had  18  of  these  [20-day  periods]  and  besides  5  days  and 
6  hours."  In  spite  of  Landa' s  statements,  however,  it  is  equally 
clear  that  had  the  Maya  attempted  to  take  note  of  these  6  additional 
hours  by  inserting  an  extra  day  in  their  calendar  every  fourth  year, 
their  day  sequence  would  have  been  disturbed  at  once.  An  examina- 
tion of  the  tonalamatl,  or  roimd  of  days  (see  pi.  5),  shows  also  that 
the  interpolation  of  a  single  day  at  any  point  would  have  thrown 
into  confusion  the  whole  Maya  calendar,  not  only  interfering  with 
the  sequence  but  also  destroying  its  power  of  reentering  itself  at  the 
end  of  260  days.  The  explanation  of  this  statement  is  found  in  the 
fact  that  the  Maya  calendar  had  no  elastic  period  corresponding  to 
our  month  of  February,  which  is  increased  in  length  whenever  the 
accumulation  of  fractional  days  necessitates  the  addition  of  an  extra 
day,  in  order  to  keep  the  calendar  year  from  gaining  on  the  true  year. 

If  the  student  can  be  made  to  realize  that  all  Maya  periods,  from 
the  lowest  to  the  highest  known,  are  always  in  a  continuous  sequence, 


MORLEY]      IITTEODUCTIOIsr  TO  STUDY  OF  MAYA  HIEROGLYPHS  45 

each  returning  into  itself  and  beginning  anew  after  completion,  he 
will  have  grasped  the  most  fmidamental  principle  of  Maya  chronol- 
ogy— its  absolute  continuity  throughout. 

It  may  be  taken  for  granted,  therefore,  in  the  discussion  to  follow 
that  no  interpolation  of  intercalary  days  was  actually  made.  It  is 
equally  probable,  however,  that  the  priests,  in  whose  hands  such 
matters  rested,  corrected  the  calendar  by  additional  calculations 
which  showed  just  how  many  days  the  recorded  year  was  ahead  of 
the  true  year  at  any  given  time.  Mr.  Bowditch  (1910:  Chap,  xi)  has 
cited  several  cases  in  which  such  additional  calculations  exactly 
correct  the  inscriptions  on  the  monument  upon  which  they  appear  and 
bring  their  dates  into  harmony  with  the  true  solar  year. 

So  far  as  the  calendar  is  concerned,  then,  the  year  consisted  of 
but  365  days.  It  was  divided  into  18  periods  of  20  days  each,  desig- 
nated in  Maya  uinal,  and  a  closing  period  of  5  days  known  as  the  xma 
IcahaJcin,  or days  without  name."  The  sum  of  these  (18x20  +  5) 
exactly  made  up  the  calendar  year. 

Table  III.  THE  DIVISIONS  OF  THE  MAYA  YEAR 


Pop 

Zac 

TJo 

Cell 

Zip 

Mac 

Zotz 

Kankin 

Tzec 

Muan 

Xul 

Pax 

Yaxkin 

Kayab 

Mol 

Cumhu 

Chen 

Uayeb 

Yax 

The  names  of  these  19  divisions  of  the  year  are  given  in  Table  III 
in  the  order  in  which  they  follow  one  another;  the  twentieth  day  of 
one  month  was  succeeded  by  the  first  day  of  the  next  month. 

The  first  day  of  the  Maya  year  was  the  first  day  of  the  month  Pop, 
which,  according  to  the  early  Spanish  authorities.  Bishop  Landa  (1864: 
p.  276)  included,  always  fell  on  the  16th  of  July.^  Uayeb,  the  last 
division  of  the  year,  contained  only  5  days,  the  last  day  of  Uayeb 
beiag  at  the  same  time  the  365th  day  of  the  year.  Consequently, 
when  this  day  was  completed,  the  next  in  order  was  the  Maya  New 
Year's  Day,  the  first  day  of  the  month  Pop,  after  which  the  sequence 
repeated  itself  as  before. 

The  xma  kaba  kin,  or  ''days  without  name,"  were  regarded  as 
especially  imlucky  and  ill-omened.  Says  Pio  Perez  (see  Landa,  1864: 
p.  384)  in  speaking  of  these  closing  days  of  the  year:  '^Some  call 
them  u  yail  Tcin  or  u  yail  Jiaah,  which  may  be  translated,  the  sorrow- 
ful and  laborious  days  or  part  of  the  year;  for  they  [the  Maya] 


1  As  Bishop  Landa  wrote  not  later  than  1579,  this  is  Old  Style.  The  corresponding  day  in  the 
Gregorian  Calendar  would  be  July  27. 


46 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


believed  that  in  them  occurred  sudden  deaths  and  pestilences,  and 
that  they  were  diseased  by  poisonous  animals,  or  devoured  by  wild 
beasts,  fearmg  that  if  they  went  out  to  the  field  to  their  labors,  some 
tree  would  pierce  them  or  some  other  kind  of  misfortune  happen  to 
them."  The  Aztec  held  the  five  closing  days  of  the  year  in  the  same 
superstitious  dread.  Persons  born  in  this  unlucky  period  were  held  to 
be  destined  by  this  fact  to  wretchedness  and  poverty  for  life.  These 
days  were,  moreover,  prophetic  in  character;  what  occurred  during 
them  continued  to  happen  ever  afterward.  Hence,  quarreling  was 
avoided  during  this  period  lest  it  should  never  cease. 

Having  learned  the  number,  length,  and  names  of  the  several 
periods  into  which  the  Maya  divided  their  year,  and  the  sequence  in 
which  these  followed  one  another,  the  next  subject  which  claims 
attention  is  the  positions  of  the  several  days  in  these  periods.  In 
order  properly  to  present  this  important  subject,  it  is  first  necessary 
to  consider  briefly  how  we  count  and  number  our  own  units  of  time, 
since  through  an  understanding  of  these  practices  we  shall  better 
comprehend  those  of  the  ancient  Maya. 

It  is  well  known  that  our  methods  of  counting  time  are  inconsistent 
with  each  other.  For  example,  in  describing  the  time  of  day,  that  is, 
in  counting  hours,  minutes,  and  seconds,  we  speak  in  terms  of  elapsed 
time.  When  we  say  it  is  1  o'clock,  in  reality  the  first  hour  after 
noon,  that  is,  the  hour  between  12  noon  and  1  p.  m.,  has  passed  and 
the  second  hour  after  noon  is  about  to  commence.  When  we  say  it 
is  2  o'clock,  in  reahty  the  second  hour  after  noon  is  finished  and  the 
third  hour  about  to  commence.  In  other  words,  we  count  the  time 
of  day  by  referring  to  passed  periods  and  not  current  periods.  This 
is  the  method  used  in  reckoning  astronomical  time.  During  the 
passage  of  the  first  hour  after  midnight  the  hours  are  said  to  be  zero, 
the  time  being  counted  by  the  number  of  minutes  and  seconds 
elapsed.  Thus,  half  past  12  is  written:  0^-  30^^^-  O^^'^-,  and  quarter  of 
1,  0^-  45°'''''  O^^'^-.  Indeed  one  hour  can  not  be  written  until  the  first 
hour  after  midnight  is  completed,  or  until  it  is  1  o'clock,  namely, 

•|^hr.  Qmin.  Qsec. 

We  use  an  entirely  different  method,  however,  in  counting  our 
days,  years,  and  centuries,  which  are  referred  to  as  current  periods 
of  time.  It  is  the  1st  day  of  January  immediately  after  midnight 
December  31.  It  was  the  first  year  of  the  Eleventh  Century  imme- 
diately after  midnight  December  31,  1000  A.  D.  And  finally,  it  was 
the  Twentieth  Century  immediately  after  midnight  December  31, 
1900  A.  D.  In  this  category  should  be  included  also  the  days  of 
the  week  and  the  months,  since  the  names  of  these  periods  also  refer 
to  present  time.  In  other  words  when  we  speak  of  our  days,  months, 
years,  and  centuries,  we  do  not  have  in  mind,  and  do  not  refer  to 
completed  periods  of  time,  but  on  the  contrary  to  current  periods. 


MORLioY]       INTEODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


47 


It  will  be  seen  that  in  the  first  method  of  counting  time',  in  speaking 
of  1  o'clock,  1  hour,  30  minutes,  we  use  only  the  cardinal  forms 
of  our  numbers;  but  in  the  second  method  we  say  the  1st  of 
January,  the  Twentieth  Century,  using  the  ordinal  forms,  though 
even  here  we  permit  ourselves  one  inconsistency.  In  speaking  of 
our  years,  which  are  reckoned  by  the  second  method,  we  say  '^nineteen 
hundred  and  twelve,"  when,  to  be  consistent,  we  should  say  nineteen 
hundred  and  twelfth,"  using  the  ordinal  ''twelfth"  instead  of  the  car- 
dinal ''twelve." 

We  may  then  summarize  our  methods  of  counting  time  as  follows : 
(1)  All  periods  less  than  the  day,  as  hours,  minutes,  and  seconds,  are 
referred  to  in  terms  of  past  time;  and  (2)  the  day  and  aU  greater 
periods  are  referred  to  in  terms  of  current  time. 

The  Maya  seem  to  have  used  only  the  former  of  these  two  methods 
in  counting  time;  that  is,  all  the  different  periods  recorded  in  the 
codices  and  the  inscriptions  seemingly  refer  to  elapsed  time  rather 
than  to  current  time,  to  a  day  passed,  rather  than  to  a  day  present. 
Strange  as  this  may  appear  to  us,  who  speak  of  our  calendar  as  current 
time,  it  is  probably  true  nevertheless  that  the  Maya,  in  so  far  as  their 
writing  is  concerned,  never  designated  a  present  day  but  always 
treated  of  a  day  gone  by.  The  day  recorded  is  yesterday  because 
to-day  can  not  be  considered  an  entity  until,  like  the  hour  of  astronom- 
ical time,  it  completes  itself  and  becomes  a  unit,  that  is,  a  yesterday. 

This  is  weU  illustrated  by  the  Maya  method  of  numbering  the 
positions  of  the  days  in  the  months,  which,  as  we  shall  see,  was 
identical  with  our  own  method  of  counting  astronomical  time.  For 
example,  the  first  day  of  the  Maya  month  Pop  was  written  Zero  Pop, 
(0  Pop)  for  not  until  one  whole  day  of  Pop  had  passed  could  the  day  1 
Pop  be  written;  by  that  time,  however,  the  first  day  of  the  month  had 
passed  and  the  second  day  commenced.  In  other  words,  the  second 
day  of  Pop  was  written  1  Pop ;  the  third  day,  2  Pop ;  the  fourth  day, 
3  Pop ;  and  so  on  through  the  20  days  of  the  Maya  month.  This 
method  of  numbering  the  positions  of  the  days  in  the  month  led  to 
calling  the  last  day  of  a  month  19  instead  of  20.  This  appears  in  Table 
ly,  in  which  the  last  6  days  of  one  year  and  the  first  22  of  the  next 
year  are  referred  to  their  corresponding  positions  in  the  divisions  of 
the  Maya  year.  It  must  be  remembered  in  using  thisTable  that  the 
closing  period  of  the  Maya  year,  the  xma  kaba  kin,  or  TJayeb,  con- 
tained only  5  days,  whereas  aU  the  other  periods  (the  18  uinals)  had 
20  days  each. 

Curiously  enough  no  glyph  for  the  tiaab,  or  year,  has  been  identified 
as  yet,  in  spite  of  the  apparent  importance  of  this  period.^  The 

1  This  is  probably  to  be  accounted  for  by  the  fact  that  in  the  Maya  system  of  chronology,  as  we  shall  see 
later,  the  36.5-day  year  was  not  used  in  recording  time.  But  that  so  fimdamental  a  period  had  therefore 
no  special  glyph  does  not  necessarily  follow,  and  the  writer  believes  the  sign  for  the  haab  will  yet  be  di^ 
covered. 


48 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


glyphs  which  represent  the  18  different  uinals  and  the  xma  kaba  kin, 
however,  are  shown  in  figures  19  and  20.  The  forms  in  figure  19  are 
taken  from  the  inscriptions  and  those  in  figure  20  from  the  codices. 

Table  IV.  POSITIONS  OF  DAYS  AT  THE  END  OF  A  YEAR 


360th  day  of  the  year 
361st  day  of  the  year 
362d  day  of  the  year 
363d  day  of  the  year 
364th  day  of  the  year 
365th  day  of  the  year 
1st  day  of  next  year 
2d  day  of  next  year 
3d  day  of  next  year 
4th  day  of  next  year 
5thday  of  next  year 
6th  day  of  next  year 
7thday  of  next  year 
8th day  of  next  year 
9th  day  of  next  year 
10th  day  of  next  year 
11th  day  of  next  year 
12th  day  of  next  year 
13th  day  of  next  year 
14th  day  of  next  year 
15th  day  of  next  year 
16th  day  of  next  year 
17th  day  of  next  year 
18th  day  of  next  year 
19th  day  of  next  year 
20th  day  of  next  year 
21st  day  of  next  year 
22d  day  of  next  year 
etc. 


19  Cumhu 

0  Uayeb 

1  Uayeb 

2  Uayeb 

3  Uayeb 

4  Uayeb 

0  Pop 

1  Pop 

2  Pop 

3  Pop 

4  Pop 

5  Pop 

6  Pop 

7  Pop 

8  Pop 

9  Pop 

10  Pop 

11  Pop 

12  Pop 

13  Pop 

14  Pop 

15  Pop 

16  Pop 

17  Pop 

18  Pop 

19  Pop 
OUo 
1  Uo 

etc. 


last  day  of  the  month  Cumhu. 
first  day  of  Uayeb. 


last  day  of  Uayeb  and  of  the  year, 
first  day  of  the  month  Pop,  and  of  the  next 
year. 


last  day  of  the  month  Pop. 
first  day  of  the  month  Uo. 


The  signs  for  the  first  four  months,  Pop,  XTo,  Zip,  and  Zotz,  show  a 
convincing  similarity  in  both  the  inscriptions  and  the  codices.  The 
essential  elements  of  Pop  (figs.  19,  a,  and  20,  a)  are  the  crossed  bands 
and  the  sign.  The  latter  is  found  in  both  the  forms  figured,  though 
only  a  part  of  the  former  appears  in  figure  20,  a.  Uo  has  two  forms 
in  the  inscriptions  (see  fig.  19,  6,  c),^  which  are,  however,  very  similar 
to  each  other  as  well  as  to  the  corresponding  forms  in  the  codices 
(fig.  20,  c).*  The  glyphs  for  the  month  Zip  are  identical  in  both 
figures  19,  d,  and  20,  d.  The  grotesque  heads  for  Zotz  in  figures  19, 
e,     and  20,  e,  are  also  similar  to  each  other.   The  essential  character- 

1  Later  researches  of  the  writer  (1914)  have  convinced  him  that  figure  19,  c,  is  not  a  sign  for  TJo,  but  a 
very  unusual  variant  of  the  sign  for  Zip,  found  only  at  Copan,  and  there  only  on  monuments  belonging 
to  the  final  period. . 

2  The  writer  was  able  to  prove  during  his  last  trip  to  the  Maya  field  that  figure  19,  /,  is  not  a  sign 
for  the  month  Zotz,  as  suggested  by  Mr.  Bowditch,  but  a  very  unusual  form  representing  Kankin. 
This  identification  is  supported  by  a  number  of  exaniples  at  Piedras  Negras, 


MORLEY]       lE^TKODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  49 


is  tic  seems  to  be  the  prominent  upturned  and  flaring  nose.  The 
forms  for  Tzec  (figs.  19,  g,  h,  and  20,  /)  show  only  a  very  general  simi- 
larity, and  those  for  Xul,  the  next  month,  are  eyen  more  unhke.  The 


KAYAB  CUMHU  UAYEB 

Fig.  19.   The  month  signs  in  the  inscriptions. 


only  sign  for  Xul  in  the  inscriptions  (fig.  19,  i,  j)  bears  yery  httle 
resemblance  to  the  common  form  for  this  month  in  the  codices  (fig. 
20,  g),  though  it  is  not  unlike  the  yariant  in  h,  figure  20.  The  essen- 
tial characteristic  seems  to  be  the  familiar  ear  and  the  small  mouth, 
shown  in  the  inscription  as  an  oyal  and  in  the  codices  as  a  hook  sur- 
rounded with  dots. 

43508°— Bull.  57—15  4 


50 


BUREAU  OF  AMERICAN"  ETHNOLOGY 


[BULL.  57 


The  sign  for  the  month  Yaxkin  is  identical  in  both  figures  19,  li,  l] 
and  20,  i,  j.  The  sign  for  the  month  Mol  in  figures  19,  m,  n,  and  20,  Jc 
exhibits  the  same  close  similarity.    The  forms  for  the  month  Chen 


a 

POP 


/ 

TZEC 


MOL 


V 
CEH 


UO 


g 


XUL 


u  V 
MUAN 


YAXKIN 


CUMHU  UAYEB 

Fig.  20.    The  month  signs  in  the  codices. 

in  figures  19,  o,  ]),  and  20,  Z,  m,  on  the  other  liand,  bear  only  a  slight 
resemblance  to  each  other.  The  forms  for  the  months  Yax  (figs.  19, 
q^,  r,  and  20,  n),  Zac  (figs.  19,  s,  t,  and  20,  o),  and  Ceh  (figs.  19,  u,  v,  and 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


51 


20,  p)  are  again  identical  in  each  case.  The  signs  for  the  next  month, 
Mac,  however,  are  entirely  dissimilar,  the  form  commonly  found  in 
the  inscriptions  (fig.  l^,w)  bearing  absolutely  no  resemblance  to  that 
shown  in  figure  20,  g',  r,  the  only  form  for  this  month  in  the  codices. 
The  yery  unusual  yariant  (fig.  19,  x),  from  Stela  25  at  Piedras  Negras 
is  perhaps  a  trifle  nearer  the  form  found  in  the  codices.  The  flat- 
tened oyal  in  the  main  part  of  the  yariant  is  somewhat  like  the  upper 
part  of  the  glyph  in  figure  20,  ^.  The  essential  element  of  the  glyph  for 
the  month  Mac,  so  far  as  the  inscriptions  are  concerned,  is  the  element 
gQD  (*)  found  as  the  superfix  in  both  w  and  x,  figure  19.    The  sign 

*  for  the  month  Kankin  (figs.  19,  y,  z,  and  20,  s,  t)  and  the  signs 
for  the  month  Muan  (figs.  19,  a',  ¥,  and  20,  u,  v)  show  only  a  gen- 
eral similarity.  The  signs  for  the  last  three  months  of  the  year,  Pax 
(figs.  19,  c',  and  20,  w),  Kayab  (figs.  19,  d'~f,  and  20,  x,  y),  and  Cumlm 
(figs.  19,  g\  V,  and  20,  z,  a' ,  V)  in  the  inscriptions  and  codices, 
respectiyely,  are  practically  identical.  The  closing  division  of  the 
year,  the  five  days  of  the  xma  kaba  kin,  called  Xlayeb,  is  represented 
by  essentially  the  same  glyph  in  both  the  inscriptions  and  the 
codices.    Compare  figure  19,  i' ,  with  figure  20,  c\ 

It  will  be  seen  from  the  foregoing  comparison  that  on  the  whole  the 
glyphs  for  the  months  in  the  inscriptions  are  similar  to  the  corre- 
sponding forms  in  the  codices,  and  that  such  variations  as  are  found 
may  readily  be  accounted  for  by  the  fact  that  the  codices  and  the 
inscriptions  probably  not  only  emanate  from  different  parts  of  the 
Maya  territory  but  also  date  from  different  periods. 

The  student  who  wishes  to  decipher  Maya  writing  is  strongly  urged 
to  memorize  the  signs  for  the  days  and  months  given  in  figures  16, 
17,  19,  and  20,  since  his  progress  will  depend  largely  on  his  ability  to 
recognize  these  glyphs  when  he  encounters  them  in  the  texts. 

The  Calendar  Kound,  or  18980-day  Period 

Before  taking  up  the  study  of  the  Calendar  Round  let  us  briefly 
summarize  the  principal  points  ascertauied  in  the  preceding  pages 
concerning  the  Maya  method  of  counting  time.  In  the  first  place 
we  learned  from  the  tonalamatl  (pi.  5)  three  things:  (1)  The  number 
of  differently  named  days;  (2)  the  names  of  these  days;  (3)  the  order 
in  which  they  invariably  followed  one  another.  And  in  the  second 
place  we  learned  in  the  discussion  of  the  Maya  year,  or  haab,  just 
concluded,  four  other  things:  (1)  The  length  of  the  year;  (2)  the 
number,  length,  and  names  of  the  several  periods  into  which  it  was 
divided;  (3)  the  order  in  which  these  periods  invariably  followed  one 
another;  (4)  the  positions  of  the  days  in  these  periods. 

The  proper  combination  of  these  two,  the  tonalamatl,  or  "round  of 
days,"  and  the  haab,  or  year  of  uinals,  and  the  xma  kaba  kin,  formed 
the  Calendar  Round,  to  which  the  tonalamatl  contributed  the  names 


52 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


of  the  days  and  the  haab  the  positions  of  these  days  in  the  divisions 
of  the  year.  The  Calendar  Round  was  the  most  important  period  in 
Maya  chronology,  and  a  comprehension  of  its  nature  and  of  the  prin- 
ciples which  governed  its  composition  is  therefore  absolutely  essential 
to  the  understanding  of  the  Maya  system  of  counting  time. 

It  has  been  explained  (see  p.  41)  that  the  complete  designation 
or  name  of  any  day  in  the  tonalamatl  consisted  of  two  equally  essen- 
tial parts:  (1)  The  name  glyph,  and  (2)  the  numerical  coefficient. 
Disregarding  the  latter  for  the  present,  let  us  first  see  wMck  of  the 
twenty  names  in  Table  I,  that  is,  the  name  parts  of  the  days,  can 
stand  at  the  beginning  of  the  Maya  year. 

In  applying  any  sequence  of  names  or  numbers  to  another  there 
are  only  three  possibilities  concerning  the  name^  or  numbers  which 
can  stand  at  the  head  of  the  resulting  sequence : 

1.  When  the  sums  of  the  units  in  each  of  the  two  sequences  contain 
no  common  factor,  each  one  of  the  units  in  turn  will  stand  at  the 
head  of  the  resulting  sequence. 

2.  When  the  sum  of  the  units  in  one  of  the  two  sequences  is  a 
multiple  of  the  sum  of  the  units  in  the  other,  only  the  first  unit 
can  stand  at  the  head  of  the  resulting  sequence. 

3.  When  the  sums  of  the  units  in  the  two  sequences  contain  a 
common  factor  (except  in  those  cases  which  fall  imder  (2),  that  is, 
in  which  one  is  a  multiple  of  the  other)  only  certain  units  can  stand  at 
the  head  of  the  sequence. 

Now,  since  our  two  numbers  (the  20  names  in  Table  I  and  the  365 
days  of  the  year)  contain  a  common  factor,  and  since  neither  is  a 
multiple  of  the  other,  it  is  clear  that  only  the  last  of  the  three  con- 
tingencies just  mentioned  concerns  us  here;  and  we  may  therefore 
dismiss  the  first  two  from  further  consideration. 

The  Maya  year,  then,  could  begin  only  with  certain  of  the  days 
in  Table  I,  and  the  next  task  is  to  find  out  which  of  these  twenty 
names  invariably  stood  at  the  beginnings  of  the  years. 

When  there  is  a  sequence  of  20  names  in  endless  repetition,  it  is 
evident  that  the  361st  will  be  the  same  as  the  1st,  since  360  =  20  X  18. 
Therefore  the  362d  will  be  the  same  as  the  2d,  the  363d  as  the  3d, 
the  364th  as  the  4th,  and  the  365  as  the  5th.  But  the  365th,  or 
5th,  name  is  the  name  of  the  last  day  of  the  year,  consequently  the 
1st  day  of  the  following  year  (the  366th  from  the  beginning)  will 
have  the  6th  name  in  the  sequence.  Following  out  this  same  idea, 
it  appears  that  the  361st  day  of  the  second  year  will  have  the  same 
name  ps  that  with  which  it  began,  that  is,  the  6th  name  in  the 
sequence,  the  362d  day  the  7th  name,  the  363d  the  8th,  the  364th 
the  9th,  and  the  365th,  or  last  day  of  the  second  year,  the  10th  name. 
Therefore  the  1st  day  of  the  third  year  (the  731st  from  the  beginning) 
will  have  the  1 1th  name  in  the  sequence.    Similarly  it  could  be  shown 


morley]      INTEODIJCTION  TO  STUDY  OF  MAYA  HIEEOGLYPHS 


53 


that  the  tMrd  year,  beginning  with  the  11th  name,  would  necessarily 
end  with  the  15th  name;  and  ihQ  fourth  year,  beginning  with  the  16th 
name  (the  1096th  from  the  beginning)  would  necessarily  end  with 
the  20th,  or  last  name,  in  the  sequence.  It  results,  therefore,  from 
the  foregoing  progression  that  the  fifth  year  will  have  to  begin  with 
the  1st  name  (the  1461st  from  the  beginning),  or  the  same  name  with 
which  t\iQ  first  year  also  began. 

This  is  capable  of  mathematical  proof,  since  the  1st  day  of  the 
fifth  year  has  the  1461st  name  from  the  beginning  of  the  sequence,  for 
1461  =  4x365+1=73x20+1.  The  1  in  the  second  term  of  this 
equation  indicates  that  the  beginning  day  of  the  fifth  year  has  been 
reached;  and  the  1  in  the  third  term  indicates  that  the  name-part 
of  this  day  is  the  1st  name  in  the  sequence  of  twenty.  In  other 
words,  every  fifth  year  began  with  a  day,  the  name  part  of  which 
was  the  same,  and  consequently  only  four  of  the  names  in  Table  I 
could  stand  at  the  beginnings  of  the  Maya  years. 

The  four  names  which  successively  occupied  this,  the  most  impor- 
tant position  of  the  year,  were:  Ik,  Manik,  Eb,  and  Caban  (see  Table  V, 
in  which  these  four  names  are  shown  in  their  relation  to  the  sequence 
of  twenty).  Beginning  with  any  one  of  these,  Ik  for  example,  the 
next  in  order,  Manik,  is  5  days  distant,  the  next,  Eb,  another  five 
days,  the  next,  Caban,  another  5  days,  and  the  next,  Ik,  the  name 
with  which  the  Table  started,  another  5  days. 

Table  V.    RELATIVE  POSITIONS  OF  DAYS  BEGINNING  MAYA  YEARS 


IK 

£B 

Akbal 

Ben 

Kan 

Ix 

Chicchan 

Men 

Cimi 

Cib 

MANIK 

CABAN 

Lamat 

Eznab 

Muluc 

Cauac 

Oc 

Ahau 

Chuen 

Imix 

Since  one  of  the  four  names  just  given  invariably  began  the  Maya 
year,  it  follows  that  in  any  given  year,  all  of  its  nineteen  divisions,  the 
18  uinals  and  the  xma  kaba  kin,  also  began  with  the  same  name, 
which  was  the  name  of  the  first  day  of  the  first  uinal.  This  is  neces- 
sarily true  because  these  1 9  divisions  of  the  year,  with  the  exception  of 
the  last,  each  contained  20  days,  and  consequently  the  name  of  the 
first  day  of  the  first  division  determined  the  names  of  the  first  days 
of  all  the  succeeding  divisions  of  that  particular  year.  Furthermore, 
since  the  xma  kaba  kin,  the  closing  division  of  the  year,  contained 
but  5  days,  the  name  of  the  first  day  of  the  following  year,  as  well  as 


54 


BUREAU  OF  AMERICAN"  ETHNOLOGY 


[BULL.  57 


the  names  of  the  first  days  of  all  of  its  divisions,  was  shifted  forward 
in  the  sequence  another  5  days,  as  shown  above. 

This  leads  directly  to  another  important  conclusion:  Since  the  first 
days  of  all  the  divisions  of  any  given  year  always  had  the  same  name- 
part,  it  follows  that  the  second  days  of  all  the  divisions  of  that  year 
had  the  same  name,  that  is,  the  next  succeeding  in  the  sequence  of 
twenty.  The  third  days  in  each  division  of  that  year  must  have  had 
the  same  name,  the  fourth  days  the  same  name,  and  so  on,  through- 
out the  20  days  of  the  month.  For  example,  if  a  year  began  with  the 
day-name  Ik,  all  of  the  divisions  in  that  year  also  began  with  the 
same  name,  and  the  second  days  of  all  its  divisions  had  the  day-name 
Akbal,  the  third  days  the  name  Kan,  the  fourth  days  the  name 
Chicclian,  and  so  forth.    This  enables  us  to  formulate  the  foUowdng^ — • 

Rule.  The  20  day-names  always  occupy  the  same  positions  in  all 
the  divisions  of  any  giveA  year. 

But  since  the  year  and  its  divisions  must  begin  with  one  of  four 
names,  it  is  clear  that  the  second  positions  also  must  be  filled -with 
one  of  another  group  of  four  names,  and  the  third  positions  with  one 
of  another  group  of  four  names,  and  so  on,  through  all  the  positions 
of  the  month.    This  enables  us  to  formulate  a  second — 

Rule.  Only  four  of  the  twenty  day-names  can  ever  occupy  any 
given  position  in  the  divisions  of  the  years. 

But  since,  in  the  years  when  Ik  is  the  1st  name,  Manik  will  be  the 
6th,  Eb  the  11th,  and  Caban  the  16th,  and  in  the  years  when  Manik 
is  the  1st,  Eb  will  be  the  6th,  Caban  the  11th,  and  Ik.  the  16th,  and 
in  the  years  when  Eb  is  the  1st,  Caban  will  be  the  6th,  Ik  the  11th,  and 
Manik  the  16th,  and  in  the  years  when  Caban  is  the  1st,  Ik  will  be 
the  6th,  Manik  the  11th,  and  Eb  the  16th,  it  is  clear  that  any  one  of 
this  group  which  begins  the  year  may  occupy  also  three  other  positions 
in  the  divisions  of  the  year,  these  positions  being  5  days  distant  from 
each  other.  Consequently,  it  follows  that  Akbal,  Lamat,  Ben,  and 
Eznab  in  Table  V,  the  names  which  occupy  the  second  positions  in 
the  divisions  of  the  year,  will  fill  the  7th,  12th,  and  17th  positions  as 
well.  Similarly  Kan,  Muluc,  Ix,  and  Cauac  will  fill  the  3d,  8th,  13th, 
and  18th  positions,  and  so  on.    This  enables  us  to  formulate  a  third^ — 

Rule.  The  20  day-names  are  divided  into  five  groups  of  four  names 
each,  any  name  in  any  group  being  five  days  distant  from  the  name 
next  preceding  it  in  the  same  group,  and  furthermore,  the  names  of 
any  one  group  will  occupy  four  different  positions  in  the  divisions  of 
successive  years,  these  positions  being  five  days  apart  in  each  case. 
This  is  expressed  in  Table  VI,  in  which  these  groups  are  shown  as 
well  as  the  positions  in  the  divisions  of  the  years  which  the  names  of 
each  group  may  occupy.  A  comparison  with  Table  V  will  demon- 
strate that  this  arrangement  is  inevitable. 


MotiLEY]      IKTEODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  55 
Table  VI.   POSITIONS  OF  DAYS  IN  DIVISIONS  OF  MAYA  YEAR 


Positions    held  by 
days  ; 

/-  1st,  6th, 
\llth, 16th 

2d,  7th, 
12th,  17th 

3d,  8th, 
13th,  18th 

4th, 9th, 
14th,  19th 

5th, 10th, 
15th.  20th 

flk 

Akbal 

Kan 

Chicchan 

Cimi 

Names  of  days  in  each 

1  Manik 

Lamat 

Muluc 

Oc 

Chuen 

group 

]Eb 

Ben 

Ix 

Men 

Cib 

icaban 

Eznab 

Cauac 

Ahau 

Imix 

But  we  have  seen  on  page  47  and  in  Table  IV  that  the  Maya  did 
not  designate  the  first  days  of  the  several  divisions  of  the  years  ac- 
cording to  our  system.  It  was  shown  there  that  the  first  day  of  Pop 
was  not  written  1  Pop,  but  0  Pop,  and  similarly  the  second  day  of 
Pop  was  written  not  2  Pop,  but  1  Pop,  and  the  last  day,  not  20  Pop, 
but  19  Pop.  Consequently,  before  we  can  use  the  names  in  Table 
VI  as  the  Maya  used  them,  we  must  make  this  shift,  keeping  in  mind, 
however,  that  Ik,  Manik,  Eb,  and  Caban  (the  only  four  of  the  twenty 
names  which  could  begin  the  year  and  which  were  written  0  Pop, 
5  Pop,  10  Pop,  or  15  Pop)  would  be  written  in  our  notation  1st  Pop, 
6th  Pop,  llth  Pop,  and  16th  Pop,  respectively.  This  difference,  as 
has  been  previously  explained,  results  from  the  Maya  method  of 
counting  time  by  elapsed  periods. 

Table  VII  shows  the  positions  of  the  days  in  the  divisions  of  the 
year  according  to  the  Maya  conception,  that  is,  with  the  shift  in  the 
month  coefficient  made  necessary  by  this  practice  of  recording  their 
days  as  elapsed  time. 

The  studejit  wiU  find  Table  VII  very  useful  in  deciphering  the  texts, 
since  it  shows  at  a  glance  the  only  positions  which  any  given  day  can 
occupy  in  the  divisions  of  the  year.  Therefore  when  the  sign  for  a 
day  has  been  recognized  in  the  texts,  from  Table  VII  can  be  ascer- 
tained the  only  four  positions  which  this  day  can  hold  in  the  month, 
thus  reducing  the  number  of  possible  month  coefficients  for  which 
search  need  be  made,  from  twenty  to  four. 


Table  VII.    POSITIONS  OF  DAYS  IN  DIVISIONS  OF  MAYA  Y^EAR 
ACCORDING  TO  MAYA  NOTATION 


t 


Positions  held  by  days  ex- 
pressed in  Maya  notation. 

jo,  5,  10, 15 

1,  6,  11, 16 

2,  7,  12,  17 

3,  8,  13,  18 

4,9,  14,  19 

flk 

Akbal 

Kan 

Chicchan 

Cimi 

Names  of  days  in  each  group 

1  Manik 

Lamat 

Muluc 

Oc 

Chuen 

|Eb 

Ben 

IX 

Men 

Cib 

ICaban 

Eznab 

Cauac 

Ahau 

Imix 

Now  let  us  summarize  the  points  which  we  have  successively 
established  as  resulting  from  the  combination  of  the  tonalamatl  and 
haab,  remembering  always  that  as  yet  we  have  been  dealing  only  with 


56 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


the  name  parts  of  the  days  and  not  their  complete  designations.  Bearing 
this  in  mind,  we  may  state  the  following  facts  concerning  the  20  day- 
names  and  their  positions  in  the  divisions  of  the  year: 

1.  The  Maya  year  and  its  several  divisions  could  begin  only  with 
one  of  these  four  day-names:  Ik,  Manik,  Eb,  and  Caban. 

2.  Consequently,  any  particular  position  in  the  divisions  of  the 
year  could  be  occupied  only  by  one  of  four  day-names. 

3.  Consequently,  every  fifth  year  any  particular  day-name  returned 
to  the  same  position  in  the  divisions  of  the  year. 

4.  Consequently,  any  particular  day-name  could  occupy  only  one 
of  four  positions  in  the  divisions  of  the  year,  each  of  which  it  held  in 
successive  years,  returning  to  the  same  position  every  fifth  year. 

5.  Consequently,  the  twenty  day-names  were  divided  into  five 
groups  of  four  day-names  each,  any  day-name  of  any  group  being 
five  days  distant  from  the  day-name  of  the  same  group  next  pre- 
ceding it. 

6.  Finally,  in  any  given  year  any  particular  day-name  occupied 
the  same  relative  position  throughout  the  divisions  of  that  year. 

Up  to  this  point,  however,  as  above  stated,  we  have  not  been  deal- 
ing with  the  complete  designations  of  the  Maya  days,  but  only  their 
name  parts  or  name  glyphs,  the  positions  of  which  in  the  several 
divisions  of  the  year  we  have  ascertained. 

It  now  remains  to  join  the  tonalamatl,  which  gives  the  complete 
names  of  the  260  Maya  days,  to  the  haab,  which  gives  the  positions 
of  the  days  in  the  divisions  of  the  year,  in  such  a  way  that  any  one 
of  the  days  whose  name-part  is  Ik,  Manik,  Eb,  or  Caban  shall  occupy 
the  first  position  of  the  first  division  of  the  year;  that  is,  0  Pop, 
or,  as  we  should  write  it,  the  first  day  of  Pop.  It  matters  little 
which  one  of  these  four  name  parts  we  choose  first,  since  in  four 
years  each  one  of  them  in  succession  will  have  appeared  in  the 
position  0  Pop. 

Perhaps  the  easiest  way  to  visualize  the  combination  of  the  tonala- 
matl and  the  haab  is  to  conceive  these  two  periods  as  two  cogwheels 
revolving  in  contact  with  each  other.  Let  us  imagine  that  the  first 
of  these,  A  (fig.  21),  has  260  teeth,  or  cogs,  each  one  of  which  is 
named  after  one  of  the  260  days  of  the  tonalamatl  and  follows  the 
sequence  shown  in  plate  5.  The  second  wheel,  B  (fig.  21),  is  some- 
what larger,  having  365  cogs.  Each  of  the  spaces  or  sockets  between 
these  represents  one  of  the  365  positions  of  the  days  in  the  divisions 
of  the  year,  beginning  with  0  Pop  and  ending  with  4  TJayeb.  See 
Table  IV  for  the  positions  of  the  days  at  the  end  of  one  year  and  the 
commencement  of  the  next.  Finally,  let  us  imagine  that  these  two 
wheels  are  brought  into  contact  with  each  other  in  such  a  way  that 
the  tooth  or  cog  named  2  Ik  in  A  shall  fit  into  the  socket  named 


MOELET]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


57 


B 


0  Pop  in  B,  after  which  both  wheels  start  to  revolve  in  the  directions 
indicated  by  the  arrows. 

The  first  day  of  the  year  whose  beginning  is  shown  at  the  point  of 
contact  of  the  two  wheels  in  figure  21  is  2  Ik  0  Pop,  that  is,  the  day 
2  Ik  which  occupies  the  first  position  in  the  month  Pop.  The  next  day 
in  succession  will  be  3  Akbal  1  Pop,  the  next  4  Kan  2  Pop,  the  next 
6  Chicchaii  3  Pop,  the  next  6  Cimi  4  Pop,  and  so  on.  As  the  wheels 
revolve  in  the  directions  indicated,  the  days  of  the  tonalamatl  succes- 
sively fall  into  their 
appropriate  p  o  s  i- 
tions  in  the  divi- 
sions of  the  year. 
Since  the  number  of 
cogs  in  A  is  smaller 
than  the  number  in 
B,  it  is  clear  that 
the  former  will 
have  returned  to 
its  starting  point, 
2  Ik  (that  is,  made 
one  complete  revo- 
lution) ,  before  the 
latter  will  have 
made  one  complete 
revolution;  and, 
further,  that  when 
the  latter  (B)  has 
returned  to  its 
starting  point,  0 
Pop,  the  corre- 
sponding cog  in  B 
will  not  be  2  Ik, 
but  another  day  (3  Manik) ,  since  by  that  time  the  smaller  wheel  will 
have  progressed  105  cogs,  or  days,  farther,  to  the  cog  3  Manik. 

The  question  now  arises,  how  many  revolutions  will  each  wheel 
have  to  make  before  the  day  2  Ik  will  return  to  the  position  0  Pop. 
The  solution  of  this  problem  depends  on  the  application  of  one 
sequence  to  another,  and  the  possibilities  concerning  the  numbers  or 
names  which  stand  at  the  head  of  the  resulting  sequence,  a  subject 
already  discussed  on  page  52.  In  the  present  case  the  numbers  in 
question,  260  and  365,  contain  a  common  factor,  therefore  our  prob- 
lem falls  under  the  third  contingency  there  presented.  Consequently, 
only  certain  of  the  260  days  can  occupy  the  position  0  Pop,  or,  in 
other  words,  cog  2  Ik  in  A  will  return  to  the  position  0  Pop  in  B  in 
fewer  than  260  revolutions  of  A.    The  actual  solution  of  the  problem 


Fig.  21.  Diagram  showing  engagement  of  tonalamatl  wheel  of  260  days  (A), 
andhaab  wheel  of  365  positions  (B);  the  combination  of  the  two  giving 
the  Calendar  Round,  or  52-year  period. 


58 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


is  a  simple  question  of  arithmetic.  Since  the  day  2  Ik  can  not  return 
to  its  original  position  in  A  until  after  260  days  shall  have  passed, 
and  since  the  day  0  Pop  can  not  return  to  its  original  position  in  B 
until  after  365  days  shall  have  passed,  it  is  clear  that  the  day  2  Ik 
0  Pop  can  not  recur  until  after  a  number  of  days  shall  have 
passed  equal  to  the  least  common  multiple  of  these  numbers,  which  is 

?^X^X5,  or  52X73X5=18,980  days.    But  18,980  days  =  52 X 
5  5 

365  =  73X260;  in  other  words  the  day  2  Ik  0  Pop  can  not  recur 
until  after  52  revolutions  of  B,  or  52  years  of  365  days  each,  and  73 
revolutions  of  A,  or  73  tonalamatls  of  260  days  each.  The  Maya 
name  for  this  52-year  period  is  unknown;  it  has  been  called  the 
Calendar  Round  by  modern  students  because  it  was  only  after  this 
interval  of  time  had  elapsed  that  any  given  day  could  return  to  the 
same  position  in  the  year.  The  Aztec  name  for  this  period  was 
xiuhmolpilli  or  toxiuhmolpia} 

The  Calendar  Round  was  the  real  basis  of  Maya  chronology,  since 
its  18,980  dates  included  all  the  possible  combinations  of  the  260  days 
with  the  365  positions  of  the  year.  Although  the  Maya  developed 
a  much  more  elaborate  system  of  counting  time,  wherein  any  date  of 
the  Calendar  Round  could  be  fixed  with  absolute  certainty  within  a 
period  of  374,400  years,  this  truly  remarkable  feat  was  accomplished 
only  by  using  a  sequence  of  Calendar  Rounds,  or  52-year  periods,  in 
endless  repetition  from  a  fixed  point  of  departure. 

In  the  development  of  their  chronological  system  the  Aztec  prob- 
ably never  progressed  beyond  the  Calendar  Round.  At  least  no 
greater  period  of  time  than  the  round  of  52  years  has  been  found  in 
their  texts.  The  failure  of  the  Aztec  to  develop  some  device  which 
would  distinguish  any  given  day  in  one  Calendar  Round  from  a  day 
of  the  same  name  in  another  has  led  to  hopeless  confusion  in  regard 
to  various  events  of  their  history.  Since  the  same  date  occurred 
at  intervals  of  every  52  years,  it  is  often  difficult  to  determine  the 
particular  Calendar  Round  to  which  any  given  date  with  its  corre- 
sponding event  is  to  be  referred;  consequently,  the  true  sequence  of 
events  in  Aztec  history  still  remains  uncertain. 

Professor  Seler  says  in  this  connection :  ^ 

Anyone  who  has  ever  taken  the  trouble  to  collect  the  dates  in  old  Mexican  history 
from  the  various  sources  must  speedily  have  discovered  that  the  chronology  is  very 
much  awry,  that  it  is  almost  hopeless  to  look  for  an  exact  chronology.  The  date  of  the 
fall  of  Mexico  is  definitely  fixed  according  to  both  the  Indian  and  the  Christian  chro- 
nology .  .  ,  but  in  regard  to  all  that  precedes  this  date,  even  to  events  tolerably  near 
the  time  of  the  Spanish  conquest,  the  statements  differ  widely. 

1  The  meanings  of  these  words  in  NahuatL,  the  language  spoken  by  the  Aztec,  are  "year  bundle  "  and  "  our 
years  will  be  bound,"  respectively.  These  doubtless  refer  to  the  fact  that  at  the  expiration  of  this  period 
the  Aztec  calendar  had  made  one  complete  round;  that  is,  the  years  were  bound  up  and  commenced  anew. 

2  Bulletin  28,  i>.  330. 


MORLET]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEEOGLYPHS 


59 


Such  confusion  indeed  is  only  to  be  expected  from  a  system  of  count- 
ing time  and  recording  events  which  was  so  loose  as  to  permit  the  occur- 
rence of  the  same  date  twice,  or  even  thrice,  within  the  span  of  a 
single  hf  e ;  and  when  a  system  so  inexact  was  used  to  regulate  the  lapse 
of  any  considerable  number  of  years,  the  possibilities  for  error  and 
misunderstanding  are  infinite.    Thus  it  was  with  Aztec  chronology. 

On  the  other  hand,  by  conceiving  the  Calendar  Rounds  to  be  in 
endless  repetition  from  a  fixed  point  of  departure,  and  measuring 
time  by  an  accurate  system,  the  Maya  were  able  to  secure  precision 
in  dating  their  events  which  is  not  surpassed 
even  by  our  own  system  of  counting  time. 

The  glyph  which  stood  for  the  Calendar 
Round  has  not  been  determined  with  any 
degree  of  certainty.  Mr.  Goodman  believes 
the  form  shown  in  figure  22,  a,  to  be  the  sign 
for  this  period,  while  Professor  Forstemann 
is  equally  sure  that  the  form  represented  by  «  & 

h  of  this  figure  expressed  the  same  idea.  fig.  22.  signs  for  the  calendar 
This_  difference  of  opinion  between  two  au-  .^roratoXS^"^ 
thorities  so  eminent  well  illustrates  the  pre- 
vailing doubt  as  to  just  what  glyph  actually  represented  the  52- 
year  period  among  the  Maya.  The  sign  in  figure  22,  a,  as  the  writer 
will  endeavor  to  show  later,  is  in  all  probability  the  sign  for  the  great 
cycle. 

As  will  be  seen  in  the  discussion  of  the  Long  Count,  the  Maya, 
although  they  conceived  time  to  be  an  endless  succession  of  Calendar 
Rounds,  did  not  reckon  its  passage  by  the  lapse  of  successive  Calendar 
Rounds;  consequently,  the  need  for  a  distinctive  glyph  which  should 
represent  this  period  was  not  acute.  The  contribution  of  the  Calendar 
Round  to  Maya  chronology  was  its  18,980  dates,  and  the  glyphs 
which  composed  these  are  found  repeatedly  in  both  the  codices  and 
the  inscriptions  (see  figs.  16,  17,  19,  20).  No  signs  have  been  found 
as  yet,  however,  for  either  the  haab  or  the  tonalamatl,  probably 
because,  like  the  Calendar  Round,  these  periods  were  not  used  as 
units  in  recording  long  stretches  of  time. 

It  will  greatly  aid  the  student  in  his  comprehension  of  the  discussion 
to  follow  if  he  will  constantly  bear  in  mind  the  fact  that  one  Calendar 
Round  followed  another  without  interruption  or  the  interpolation  of 
a  single  day;  and  further,  that  the  Calendar  Round  may  be  likened 
to  a  large  cogwheel  having  18,980  teeth,  each  one  of  which  repre- 
sented one  of  the  dates  of  this  period,  and  that  this  wheel  revolved 
forever,  each  cog  passing  a  fixed  point  once  every  52  years. 


60 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


The  Long  Count 

We  have  seen : 

1 .  How  the  Maya  distinguished  1  day  from  the  259  others  in  the 
tonalamatl ; 

2.  How  they  distinguished  the  position  of  1  day  from  the  364 
others  in  the  haab,  or  year;  and,  finally, 

3.  How  by  combining  (1)  and  (2)  they  distinguished  1  day  from 
the  other  18,979  of  the  Calendar  Round. 

It  remains  to  explain  how  the  Maya  insured  absolute  accuracy  in 
fixing  a  day  within  a  period  of  374,400  years,  as  stated  above,  or  how 
they  distinguished  1  day  from  136,655,999  others. 

The  Calendar  Round,  as  we  have  seen,  determined  the  position  of  a 
given  day  within  a  period  of  only  52  years.  Consequently,  in  order 
to  prevent  confusion  of  days  of  the  same  name  in  successive  Calendar 
Rounds  or,  in  other  words,  to  secure  absolute  accuracy  in  dating 
events,  it  was  necessary  to  use  additional  data  in  the  description  of 
any  date. 

In  nearly  all  systems  of  chronology  that  presume  to  deal  with  really 
long  periods  the  reckoning  of  years  proceeds  from  fixed  starting 
points.  Thus  in  Christian  chronology  the  starting  point  is  the  Birth 
of  Christ,  and  our  years  are  reckoned  as  B.  C.  or  A.  D.  according 
as  they  precede  or  follow  this  event.  The  Greeks  reckoned  time 
from  the  earliest  Olympic  Festival  of  which  the  winner's  name  was 
known,  that  is,  the  games  held  in  776  B.  C,  which  were  won  by 
a  certain  Coroebus.  The  Romans  took  as  their  starting  point  the 
supposed  date  of  the  foundation  of  Rome,  753  B.  C.  The  Baby- 
lonians counted  time  as  beginning  with  the  Era  of  Nabonassar,  747 
B.  C.  The  death  of  Alexander  the  Great,  in  325  B.  C,  ushered  in 
the  Era  of  Alexander.  With  the  occupation  of  Babylon  in  311  B.  C. 
by  Seleucus  Nicator  began  the  so-called  Era  of  Seleucidse.  The  con- 
quest of  Spain  by  Augustus  Caesar  in  38  B.  C.  marked  the  beginning 
of  a  chronology  which  endured  for  more  than  fourteen  centuries. 
The  Mohammedans  selected  as  their  starting  point  the  flight  of  their 
prophet  Mohammed  from  Mecca  in  622  A.  D.,  and  events  in  this 
chronology  are  described  as  having  occurred  so  many  years  after  the 
Hegira  (The  Flight).  The  Persian  Era  began  with  the  date  632 
A.  D.,  in  which  year  Yezdegird  III  ascended  the  throne  of  Persia. 

It  will  be  noted  that  each  of  the  above-named  systems  of  chro- 
nology has  for  its  starting  point  some  actual  historic  event,  the  occur- 
rence, if  not  the  date  of  which,  is  indubitable.  Some  chronologies, 
however,  commence  with  an  event  of  an  altogether  different  charac- 
ter, the  date  of  which  from  its  very  nature  must  always  remain 
hypothetical.  In  this  class  should  be  mentioned  such  chronologies  as 
reckon  time  from  the  Creation  of  the  World.  For  example,  the  Era 
of  Constantinople,  the  chronological  system  used  in  the  Greek  Church, 


MORLET]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  61 


commences  with  that  event,  supposed  to  have  occurred  in  5509  B.  C. 
The  Jews  reckoned  the  same  event  as  having  taken  place  in  3761 
B.  C.  and  begin  the  counting  of  time  from  this  point.  A  more  f  amiUar 
chronology,  having  for  its  starting  point  the  Creation  of  the  World,  is 
that  of  Archbishop  Usher,  in  the  Old  Testament,  which  assigns  this 
event  to  the  year  4004  B.  C. 

In  common  with  these  other  civilized  peoples  of  antiquity  the 
ancient  Maya  had  realized  in  the  development  of  their  chronological 
system  the  need  for  a  fixed  starting  point,  from  which  all  subsequent 
events  could  be  reckoned,  and  for  this  purpose  they  selected  one  of 
the  dates  of  their  Calendar  Round.  This  was  a  certain  date,  4  Ahau 
8  Cumhu,^  that  is,  a  day  named  4  Ahau,  which  occupied  the  9th  posi- 
tion in  the  month  Cumlm,  the  next  to  last  division  of  the  Maya  year 
(see  Table  III). 

While  the  nature  of  the  event  which  took  place  on  this  date  ^  is  un- 
known, its  selection  as  the  point  from  which  time  was  subsequently 
reckoned  alone  indicates  that  it  must  have  been  of  exceedingly  great 
importance  to  the  native  mind.  In  attempting  to  approximate  its 
real  character,  however,  we  are  not  without  some  assistance  from  the 
codices  and  the  inscriptions.  For  instance,  it  is  clear  that  all  Maya 
dates  which  it  is  possible  to  regard  as  contemporaneous  ^  refer  to  a  time 
fully  3,000  years  later  than  the  starting  point  (4  Ahau  8  Cumhu)  from 
which  each  is  reckoned.  In  other  words,  Maya  history  is  a  blank 
for  more  than  3,000  years  after  the  initial  date  of  the  Maya  chrono- 
logical system,  during  which  time  no  events  were  recorded. 

This  interesting  condition  strongly  suggests  that  the  starting 
point  of  Maya  chronology  was  not  an  actual  historical  event,  as  the 
founding  of  Rome,  the  death  of  Alexander,  the  birth  of  Christ,  or 
the  flight  of  Mohammed  from  Mecca,  but  that  on  the  contrary  it  was 
a  purely  hypothetical  occurrence,  as  the  Creation  of  the  World  or  the 
birth  of  the  gods;  and  further,  that  the  date  4  Ahau  8  Cumhu  was 
not  chosen  as  the  starting  point  until  long  after  the  time  it  desig- 
nates. This,  or  some  similar  assumption,  is  necessary  to  account 
satisfactorily  for  the  observed  facts: 

1.  That,  as  stated,  after  the  starting  point  of  Maya  chronology  there 
is  a  silence  of  more  than  3,000  years,  unbroken  by  a  single  contem- 
poraneous record,  and 

1  All  Initial  Series  now  known,  with  the  exception  of  two,  have  the  date  4  Ahau  8  Cumhu  as  their  com- 
mon point  of  departure.  The  two  exceptions,  the  Initial  Series  on  the  east  side  of  Stela  C  at  Quirigua 
and  the  one  on  the  tablet  in  the  Temple  of  the  Cross  at  Palenque,  proceed  from  the  date  4  Ahau  8  Zotz— 
more  than  5,000  years  in  advance  of  the  starting  point  just  named.  The  writer  has  no  suggestions  to  offer 
in  explanation  of  these  two  dates  other  than  that  he  believes  they  refer  to  some  mythological  event.  For 
instance,  in  the  belief  of  the  Maya  the  gods  may  have  been  born  on  the  day  4  Ahau  8  Zotz,  and  5,000 
years  later  approximately  on  4  Ahau  8  Cumhu  the  world,  including  mankind,  may  have  been  created. 

2  Some  writers  have  called  the  date  4  Ahau  8  Cumhu,  the  normal  date,  probably  because  it  is  the  stand- 
ard date  from  wl.ich  practically  all  Maya  calculations  proceed.  The  writer  has  not  followed  this  practice, 
however. 

2  That  is,  dates  which  signified  present  time  when  they  were  recorded, 


62 


BUREAU  OF  AMERICAN  ETHNOLOGY 


Lbull,  57 


2.  That  after  this  long  period  had  elapsed  all  the  dated  monuments^ 
had  their  origin  in  the  comparatively  short  period  of  four  centuries. 

Consequently,  it  is  safe  to  conclude  that  no  matter  what  the  Maya 
may  have  believed  took  place  on  this  date  4  Ahau  8  Cumhu,  in  reality 
when  this  day  was  present  time  they  had  not  developed  their  dis- 
tinctive civilization  or  even  achieved  a  social  organization. 

It  is  clear  from  the  foregoing  that  in  addition  to  the  Calendar 
Round,  the  Maya  made  use  of  a  fixed  starting  point  in  describing 
their  dates.  The  next  question  is,  Did  they  record  the  lapse  of  more 
than  3,000  years  simply  by  using  so  unwieldy  a  unit  as  the  52-year 
period  or  its  multiples?  A  numerical  system  based  on  52  as  its 
primary  unit  immediately  gives  rise  to  exceedingly  awkward  num- 
bers for  its  higher  terms;  that  is,  52,  104,  156,  208,  260,  312,  etc. 
Indeed,  the  expression  of  really  large  numbers  in  terms  of  52  involves 
the  use  of  comparatively  large  multipliers  and  hence  of  more  or  less 
intricate  multiplications,  since  the  unit  of  progression  is  not  decimal 
or  even  a  multiple  thereof.  The  Maya  were  far  too  clever  mathema- 
ticians to  have  been  satisfied  with  a  numerical  system  which  employed 
units  so  inconvenient  as  52  or  its  multiples,  and  which  invotved 
processes  so  clumsy,  and  we  may  therefore  dismiss  the  possibility  of 
its  use  without  further  consideration. 

In  order  to  keep  an  accurate  account  of  the  large  numbers  used  in 
recording  dates  more  than  3,000  years  distant  from  the  starting  point, 
a  numerical  system  was  necessary  whose  terms  could  be  easily 
handled,  like  the  units,  tens,  hundreds,  and  thousands  of  our  own 
decimal  system.  Whether  the  desire  to  measure  accurately  the 
passage  of  time  actually  gave  rise  to  their  numerical  system,  or  vice 
versa,  is  not  known,  but  the  fact  remains  that  the  several  periods 
of  Maya  chronology  (except  the  tonalamatl,  haab,  and  Calendar 
Round,  previously  discussed)  are  the  exact  terms  of  a  vigesimal  sys- 
tem of  numeration,  with  but  a  single  exception.    (See  Table  VIII.) 

Table  VIII.  THE  MAYA  TIME-PERIODS 

1  kin  =  1  day 

20  kins     =1  uinal         =  20  days 

18  uinals  =1  tun  =         360  days 

20  tuns  =1  katun  =  7,200  days 
20  katuns  =1  cycle  =  144,000  days 
202  cycles=l  great  cycle =2,880,000  days 

Table  VIII  shows  the  several  periods  of  Maya  chronology  by  means 
of  which  the  passage  of  time  was  measured.  All  are  the  exact  terms 
of  a  vigesimal  system  of  numeration,  except  in  the  2d  place  (uinals) , 

•  This  statement  does  not  take  account  of  the  Tuxtla  Statuette  and  the  Holactun  Initial  Series,  which 
extend  the  range  of  the  dated  monuments  to  ten  centuries. 

^  For  the  discussion  of  the  number  of  cycles  in  a  great  cycle,  a  question  concerning  which  there  are 
two  different  opinions,  see  pp.  107  et  seq. 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


63 


in  which  18  units  instead  of  20  make  1  unit  of  the  Bd  place,  or 
order  next  higher  (tuns) .  The  break  in  the  regularity  of  the  viges- 
imal progression  in  the  3d  place  was  due  probably  to  the  desire  to 
bring  the  unit  of  this  order  (the  tun)  into  agreement  with  the  solar 
year  of  365  days,  the  number  360  being  much  closer  to  365  than  400, 
the  third  term  of  a  constant  vigesimal  progression.  We  have  seen  on 
page  45  that  the  18  uinals  of  the  haab  were  equivalent  to  360  days 
or  kins,  precisely  the  number  contained  in  the  third  term  of  the 
above  table,  the  tun.  The  fact  that  the  haab,  or  solar  year,  was 
composed  of  5  days  more  than  the  tun,  thus  causing  a  discrepancy 
of  5  days  as  compared  with  the  third  place  of  the  chronological  sys- 
tem, may  have  given  to  these  5  closing  days  of  the  haab — that  is,  the 
xma  kaba  kin — the  unlucky  character  they  were  reputed  to  possess. 

The  periods  were  numbered  from  0  to  19,  inclusive,  20  units  of 
any  order  (except  the  2d)  always  appearing  as  1  unit  of  the  order 
next  higher.  For  example,  a  number  involving  the  use  of  20  kins 
was  written  1  uinal  instead. 

We  are  now  in  possession  of  all  the  different  factors  which  the 
Maya  utilized  in  recording  their  dates  and  in  counting  time : 

1.  The  names  of  their  dates,  of  which  there  could  be  only  18,980 
(the  number  of  dates  in  the  Calendar  Round) . 

2.  The  date,  or  starting  point,  4  Ahau  8  Cumliu,  from  which  time 
was  reckoned. 

3.  The  counters,  that  is,  the  units,  used  in  measuring  the  passage 
of  time. 

It  remains  to  explain  how  these  factors  were  combined  to  express 
the  various  dates  of  Maya  chronology. 

Initial  Series 

The  usual  manner  in  which  dates  are  written  in  both  the  codices  and 
the  inscriptions  is  as  follows:  First,  there  is  set  down  a  number  com- 
posed of  five  periods,  that  is,  a  certain  number  of  cycles,  katuns,  tuns, 
uinals,  and  kins,  which  generally  aggregate  between  1,300,000  and 
1,500,000  days;  and  this  number  is  followed  by  one  of  the  18,980 
dates  of  the  Calendar  Round.  As  we  shall  see  in  the  next  chapter, 
if  this  large  number  of  days  expressed  as  above  be  counted  forward 
from  the  fixed  starting  point  of  Maya  chronology,  4  Ahau  8  Cumliu, 
the  date  invariably  ^  reached  will  be  found  to  be  the  date  written 
at  the  end  of  the  long  number.  This  method  of  dating  has  been 
called  the  Initial  Series,  because  when  inscribed  on  a  monument  it 
invariably  stands  at  the  liead  of  the  inscription. 

The  student  will  better  comprehend  this  Initial-series  method  of 
dating  if  he  will  imagine  the  Calendar  Round  represented  by  a  large 
cogwheel  A,  figure  23,  having  18,980  teeth,  each  one  of  which  is 


1  There  are  only  two  known  exceptions  to  this  statement,  namely,  the  Initial  Series  on  the  Temple  of 
the  Cross  at  Palenque  and  that  on  the  east  side  of  Stela  C  at  Quirigua,  already  noted. 


64 


BUKEAU  OF  AMERICAN  ETHNOLOGY 


[BULL.57 


named  after  one  of  the  dates  of  the  calendar.  Furthermore,  let  him 
suppose  that  the  arrow  B  in  the  same  figure  points  to  the  tooth,  or 
cog,  named  4  Ahau  8  Cumliu;  and  finally  that  from  this  as  its  original 
position  the  wheel  commences  to  revolve  in  the  direction  indicated 
by  the  arrow  in  A. 

It  is  clear  that  after  one  complete  revolution  of  A,  18,980  days  will 
have  passed  the  starting  point  B,  and  that  after  two  revolutions 

37,960  days  will  have 


B  ^ — ^ 


'°c 

nau  eCumhu 


passed,  and  after  three, 
56,940,  and  so  on.  In- 
deed, it  is  only  a  question 
of  the  number  of  revolu- 
tions of  A  until  as  many  as 
1,500,000,  or  any  number 
of  days  in  fact,  will  have 
passed  the  starting  point 
B,  or,  in  other  words,  will 
have  elapsed  since  the  in- 
itial date,  4  Ahau  8  Cumliu. 
This  is  actually  what  hap- 
pened according  to  the 
Maya  conception  of  time. 

For  example,  let  us  im- 
agine that  a  certain  Initial 
Series  expresses  in  terms 
of  cycles,  katuns,  tuns, 
uinals,  and  kins,  the  num- 
ber 1,461,463,  and  that  the 
date  recorded  by  this  num- 
ber of  days  is  7  Akbal  11  Cumliu.  Referring  to  figure  23,  it  is  evi- 
dent that  77  revolutions  of  the  cogwheel  A,  that  is,  77  Calendar 
Rounds,  will  use  up  1,461,460  of  the  1,461,463  days,  since  77  X  18,980 
=  1,461,460.  Consequently,  when  77  Calendar  Rounds  shall  have 
passed  we  shall  still  have  left  3  days  (1,461,463-  1,461,460  =  3), 
which  must  be  carried  forward  into  the  next  Calendar  Round.  The 
1,461,461st  day  will  be  5  Imix  9  Cumliu,  that  is,  the  day  following  4 
Ahau  8  Cumhu  (see  fig.  23) ;  the  l,461,462d  day  will  be  6  Ik  10  Cumhu, 
and  the  1,461,463d  day,  the  last  of  the  days  in  our  Initial  Series, 
7  Akbal  11  Cumhu,  the  date  recorded.  Examples  of  this  method  of 
dating  (by  Initial  Series)  will  be  given  in  Chapter  V,  where  this  sub- 
ject will  be  considered  in  greater  detail. 


Fig.  23.   Diagram  showing  section  of  Calendar-round  wheel. 


THE  INTRODUCING  GLYPH 


In  the  inscriptions  an  Initial  Series  is  invariably  preceded  by  the 
so-called  '4ntrQd\jcing  glyph,"  the  Maya  name  for  which  is  unknown. 


MORLEY]      INTRODUCTION"  TO  STUDY  OF  MAYA  HIEROGLYPHS 


65 


Several  examples  of  this  glyph  are  shown  in  figure  24.  This  sign  is 
composed  of  four  constant  elements: 

1.  The  trinal  superfix. 

2.  The  pair  of  comblike  lateral  appendages. 

3.  The  tun  sign  (see  fig.  29,  a,  h). 

4.  The  trinal  subfix. 

In  addition  to  these  four  constant  elements  there  is  one  variable 
element  which  is  always  found  between  the  pair  of  comblike  lateral 
appendages.  In  figure  24,  a,  h,  this  is  a  grotesque  head;  in  c,  a 
natural  head;  and  in  d,  one  of  the  20  day-signs,  Ik,  This  element 
varies  greatly  throughout  the  inscriptions,  and,  judging  from  its 
central  position  in  the  ^introducing  glyph  "  (itself  the  most  prominent 
character  in  every  inscription  in  which  it  occurs),  it  must  have  had 
an  exceedingly  important  meaning.^  A  variant  of  the  comblike 
appendages  is  shown  in  figure  24,  c,  e,  in  which  these  elements  are 


d  e  f 

Fig.  24.   Initial-series  '^introducing  glyph." 


replaced  by  a  pair  of  fishes.  However,  in  such  cases,  all  of  which 
occur  at  Cop  an,  the  treatment  of  the  fins  and  tail  of  the  fish  strongly 
suggests  the  elements  they  replace,  and  it  is  not  improbable,  there- 
fore, that  the  comblike  appendages  of  the  ^introducing  glyph''  are 
nothing  more  nor  less  than  conventionalized  fish  fins  or  tails ;  in  other 
words,  that  they  are  a  kind  of  glyphic  synecdoche  in  which  a  part 
(the  fin)  stands  for  the  whole  (the  fish).  That  the  original  form  of 
this  element  was  the  fish  and  not  its  conventionalized  fin  (*)  seems  |j 
to  be  indicated  by  several  facts:  (1)  On  Stela  D  at  Copan,  where  * 
only  full-figure  glyphs  are  presented,^  the  two  comblike  appendages  of 
the  'introducing  glyph"  appear  unmistakably  as  two  fishes.  (2)  In 
some  of  the  earliest  stelse  at  Copan,  as  Stelae  15  and  P,  while  these 
elements  are  not  fish  forms,  a  head  (fish  ?)  appears  with  the  conven- 
tionalized comb  element  in  each  case.  The  writer  believes  the  inter- 
pretation of  this  phenomenon  to  be,  that  at  the  early  epoch  in  which 


1  Mr.  Bowditcb  (1910:  App.  VIII,  310-18)  discusses  the  possible  meanings  of  this  element. 

2  For  explanation  of  the  term  ''full-figure  glyphs/'  see  p.  67, 

43508°— Bull.  57—15  5 


66 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


Stelae  15  and  P  were  erected  the  conventionalization  of  the  element 
in  question  had  not  been  entirely  accomplished,  and  that  the  head 
was  added  to  indicate  the  form  from  which  the  element  was  derived. 
(3)  If  the  fish  was  the  original  form  of  the  combhke  element  in  the 
'introducing  glyph/'  it  was  also  the  original  form  of  the  same  element 
in  the  katun  glyph.  (Compare  the  comb  elements  (f)  in  figures  27,  g 
a,  h,  Bj  and  24,  a,  h,  d  with  each  other.)  If  this  is  true,  a  natural  t 
explanation  for  the  use  of  the  fish  in  the  katun  sign  lies  near  at  hand. 
As  previously  explained  on  page  28,  the  comblike  element  stands  for 
the  sound  ca  (c  hard) ;  while  Ml  in  Maya  means  20.  Also  the  element 
^^^^  (**)  stands  for  the  sound  tun.  Therefore  catun  or  katun  means  20 
tuns.  But  the  Maya  word  for  ''fish,"  cay  (c  hard)  is  also  a  close 
phonetic  approximation  of  the  sound  ca  or  leal.  Consequently,  the 
fish  sign  may  have  been  the  original  element  in  the  katun  glyph^ 
H  which  expressed  the  concept  20,  and  which  the  conventionalization 
tt  of  glyphic  forms  gradually  reduced  to  the  element  (ft)  without 
destroying,  however,  its  phonetic  value. 

Without  pressing  this  point  further,  it  seems  not  unhkely  that  the 
combhke  elements  in  the  katun  glyph,  as  weU  as  in  the  ''introducing 
glyph,"  may  well  have  been  derived  from  the  fish  sign. 

Turning  to  the  codices,  it  must  be  admitted  that  in  spite  of  the  fact 
that  many  Initial  Series  are  found  therein,  the  "introducing  glyph" 
has  not  as  yet  been  positively  identified.  It  is  possible,  however,  that 
the  sign  shown  in  figure  24,/,  may  be  a  form  of  the  ''introducing 
glyph";  at  least  it  precedes  an  Initial  Series  in  four  places  in  the 
Dresden  Codex  (see  pi.  32).  It  is  composed  of  the  trinal  superfix 
and  a  conventionalized  fish  (?). 

Mr.  Goodman  calls  this  glyph  (fig.  24,  a-e)  the  sign  for  the  great 
cycle  or  unit  of  the  6th  place  (see  Table  VIII).  He  bases  this  identi- 
fication on  the  fact  that  in  the  codices  units  of  the  6th  place  stand 
immediately  above  ^  units  of  the  5th  place  (cycles),  and  consequently 
since  this  glyph  stands  immediately  above  the  units  of  the  5th  place 
in  the  inscriptions  it  must  stand  for  the  units  of  the  6th  place.  While 
admitting  that  the  analogy  here  is  close,  the  writer  nevertheless  is 
inclined  to  reject  Mr.  Goodman's  identification  on  the  following 
grounds:  (1)  This  glyph  never  occurs  with  a  numerical  coefficient, 
while  units  of  all  the  other  orders — that  is,  cycles,  katuns,  tuns,  uinals, 
and  kins  are  never  without  them.  (2)  Units  of  the  6th  order  in  the 
codices  invariably  have  a  numerical  coefficient,  as  do  all  the  other 
orders.  (3)  In  the  only  three  places  in  the  inscriptions^  in  which  six 
periods  are  seemingly  recorded,  though  not  as  Initial  Series,  the  6th 
period  has  a  numerical  coefficient  just  as  have  the  other  five,  and, 

1  See  the  discussion  of  Serpent  numbers  in  Chapter  VI. 

2  These  three  inscriptions  are  found  on  Stela  N,  west  side,  at  Copan,  the  tablet  of  the  Temple  of  the  In- 
scriptions at  Palenque,  and  Stela  10  at  Tikal.   For  the  discussion  of  these  inscriptions,  see  pp.  114-127. 


MORLEY]      INTEODUCTIOI^  TO  STUDY  OF  MAYA  HIEROGLYPHS  67 

moreover,  the  glyph,  in  the  6th  position  is  unhke  the  forms  in  figure 
24.  (4)  Five  periods,  not  six,  in  every  Initial  Series  express  the  dis- 
tance from  the  starting  point,  4  Ahau  8  Cumhu,  to  the  date  recorded 
at  the  end  of  the  long  numbers. 

It  is  probable  that  when  the  meaning  of  the  '^introducing  glyph" 
has  been  determined  it  will  be  found  to  be  quite  apart  from  the 
numerical  side  of  the  Initial  Series^  at  least  in  so  far  as  the  distance 
of  the  terminal  date  from  the  starting  point,  4  Ahau  8  Cumliu,  is 
concerned. 

While  an  Initial  Series  in  the  inscriptions,  as  has  been  previously 
explained,  is  invariably  preceded  by  an  'introducing  glyph,"  the 
opposite  does  not  always  obtain.  Some  of  the  very  earliest  monu- 
ments at  Copan,  notably  Stelae  15,  7,  and  P,  have  ''introducing 
glyphs"  inscribed  on  two  or  three  of  their  four  sides,  although  but 
one  Initial  Series  is  recorded  on  each  of  these  monuments.  Examples 
of  this  use  of  the  "introducing  glyph,"  that  is,  other  than  as  standing 
at  the  head  of  an  Initial  Series,  are  confined  to  a  few  of  the  earliest 
monuments  at  Copan,  and  are  so  rare  that  the  beginner  will  do  well 
to  disregard  them  altogether  and  to  follow  this  general  rule :  That  in 
the  inscriptions  a  glyph  of  the  form  shown  in  figure  24,  a-e,  will 
invariably  be  followed  by  an  Initial  Series. 

Having  reached  the  conclusion  that  the  introducing  glyph  was  not 
a  sign  for  the  period  of  the  6th  order,  let  us  next  examine  the  signs 
for  the  remaining  orders  or  periods  of  the  chronological  system 
(cycles,  katuns,  tuns,  uinals,  and  kins) ,  constantly  bearing  in  mind 
that  these  five  periods  alone  express  the  long  numbers  of  an  Initial 
Series.* 

Each  of  the  above  periods  has  two  entirely  different  glyphs  which 
may  express  it.  These  have  been  called  (1)  The  normal  form;  (2) 
The  head  variant.  In  the  inscriptions  examples  of  both  these  classes 
occur  side  by  side  in  the  same  Initial  Series,  seemingly  according  to 
no  fixed  rule,  some  periods  being  expressed  by  their  normal  forms  and 
others  by  their  head  variants.  In  the  codices,  on  the  other  hand,  no 
head-variant  period  glyphs  have  yet  been  identified,  and  although 
the  normal  forms  of  the  period  glyphs  have  been  found,  they  do  not 
occur  as  imits  in  Initial  Series. 

As  head  variants  also  should  be  classified  the  so-called  "full-figure 
glyphs,"  in  which  the  periods  given  in  Table  VIII  are  represented  by 
full  figures  instead  of  by  heads.  In  these  forms,  however,  only  the 
heads  of  the  figures  are  essential,  since  they  alone  present  the  deter- 
mining characteristics,  by  means  of  which  in  each  case  identification 
is  possible.  Moreover,  the  head  part  of  any  full-figure  variant  is 
characterized  by  precisely  the  same  essential  elements  as  the  corre- 


1  The  discussion  of  glyphs  which  may  represent  the  great  cycle  or  period  of  the  6th  order  will  be  pre- 
sented on  pp.  114-127  in  connection  with  the  discussion  of  numbers  having  six  or  more  orders  of  units. 


68 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


spending  head  variant  for  the  same  period,  or  in  other  words,  the 
ackUtion  of  the  body  parts  in  full-figure  glyphs  in  no  way  influences 
or  changes  their  meanings.  For  this  reason  head-variant  and  full- 
figure  forms  have  been  treated  together.  These  full-figure  glyphs 
are  exceedingly  rare,  having  been  found  only  in  five  Initial  Series 
throughout  the  Maya  area:  (1)  On  Stela  D  at  Copan;  (2)  on  Zoo- 
morph  B  at  Quirigua;  (3)  on  east  side  Stela  D  at  Quirigua;  (4)  on 
west  side  Stela  D  at  Quirigua;  (5)  on  Hieroglyphic  Stairway  at 
Copan.  A  few  full-figure  glyphs  have  been  found  also  on  an  oblong 
altar  at  Copan,  though  not  as  parts  of  an  Initial  Series,  and  on  Stela 
15  as  a  period  glyph  of  an  Initial  Series. 

THE  CYCLE  GLYPH 

The  Maya  name  for  the  period  of  the  5th  order  in  Table  VIII  is 
unknown.    It  has  been  called    the  cycle,"  however,  by  Maya  stu- 


d  e  f 

Fig.  25.   Signs  for  the  cycle:  a-c,  Normal  forms;  d-f,  head  variants. 


dents,  and  in  default  of  its  true  designation,  this  name  has  been 
generally  adopted.  The  normal  form  of  the  cycle  glyph  is  shown  in 
figure  25,  a,  h,  c.  It  is  composed  of  an  element  which  appears  twice 
over  a  knotted  support.  The  repeated  element  occurs  also  in  the  signs 
for  the  months  Chen,  Yax,  Zac,  and  Ceh  (see  figs.  19,  o-v,  20,  l-p) . 
This  has  been  called  the  Cauac  element  because  it  is  similar  to  the 
sign  for  the  day  Cauac  in  the  codices  (fig.  17,  ¥),  though  on  rather 
inadequate  grounds  the  writer  is  inclined  to  believe.  The  head  variant 
of  the  cycle  glyph  is  shown  in  figure  25,  d-f.  The  essential  charac- 
teristic of  this  grotesque  head  with  its  long  beak  is  the  hand  element 
6^  (*) ,  which  forms  the  lower  jaw,  though  in  a  very  few  instances  even 
*  this  is  absent.  In  the  full-figure  forms  this  same  head  is  joined 
to  the  body  of  a  bird  (see  fig.  26).  The  bird  intended  is  clearly  a 
parrot,  the  feet,  claws,  and  beak  being  portrayed  in  a  very  realistic 
manner.    No  glyph  for  the  cycle  has  yet  been  found  in  the  codices. 

THE  KATUN  GLYPH 

The  period  of  the  4ch  place  or  order  was  called  by  the  Maya  the 
Jcatun;  that  is  to  say,  20  tuns,  since  it  contained  20  units  of  the  3d 


morley]      iNTKODUCTIOiSr  TO  STUDY  OF  MAYA  HIEROGLYPHS 


69 


order  (see  Table  VIII) .  The  normal  form  of  the  katun  glyph  is 
shown  in  figure  27,  a-d.  It  is  composed  of  the  normal  form  of  the  tun 
sign  (fig.  29,  a,  h)  surmounted  by  the  pair  of  comb- 
like  appendages,  which  we  have  elsewhere  seen  meant 
20,  and  which  were  probably  derived  from  the  repre- 
sentation of  a  fish.  The  whole  glyph  thus  graph- 
ically portrays  the  concept  20  tuns,  which  according 
to  Table  VIII  is  equal  to  1  katun.  The  normal 
form  of  the  katun  glyph  in  the  codices  (fig.  27,  c,  d) 
is  identical  with  the  normal  form  in  the  inscriptions 
(fig.  27,  a,  h) .  Several  head  variants  are  found.  The 
most  easily  recognized,  though  not  the  most  com- 
mon, is  shown  in  figure  27,  e,  in  which  the  superfix 
is  the  same  as  in  the  normal  form;  that  is,  the  ele- 
i@S  ^^^^  (t);  which  probably  signifies  20  in  this  connection.  To 
t  be  logical,  therefore,  the  head  element  should  be  the  same 
as  the  head  variant  of  the  tun  glyph,  but  this  is  not  the  case  (see  fig. 
29,  e-li) .  When  this  superfix  is  present,  the  identification  of  the  head 
variant  of  the  katun  glyph  is  an  easy  matter,  but  when  it  is  absent 


Fig.  26.  FuU-figure 
variant  of  cycle  sign. 


d 

1 

e  f  g  h 

Fig.  27.   Signs  for  the  katun:  a-d,  Normal  forms;  e-Ji,  head  variants. 

it  is  difficult  to  fix  on  any  essential  characteristic.  The  general 
shape  of  the  head  is  like  the  head  variant  of  the  cycle  glyph.  Perhaps 
the  oval  (**)  in  the  top  of  the  head  in  figure  27, /-A,  and  c;^^ 
the  small  curUng  fang  (f f )  represented  as  protruding  from  **  tt 
the  back  part  of  the  mouth  are  as  constant  as  any  of  the  other 
elements.  The  head  of  the  full-figure  variant  in  figure  28  presents 
the  same  lack  of  essential  characteristics  as  the  head  variant,  though 
in  this  form  the  small  curling  fang  is  also  found.  Again,  the  body 
attached  to  this  head  is  that  of  a  bird  which  has  been  identified  as 
an  eagle. 


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BUKEAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


THE   TUN  GLYPH 


The  period  of  the  3d  place  or  order  was  called  by  the  Maya  the 
tun,  which  means  ''stone/'  possibly  because  a  stone  was  set  up  every 
360  days  or  each  tun  or  some  multiple  thereof.  Com- 
pare so-called  hotun  or  katun  stones  described  on  page 
34.    The  normal  sign  for  the  tun  in  the  inscriptions 
(see  fig.  29,  a,  h)  is  identical  with  the  form  found  in 
the  codices  (see  fig.  29,  c).    The  head  variant,  which 
bears  a  general  resemblance  to  the  head  variant  for 
Fig  28  Full-         cyclc  and   katun,  has  several  forms.    The  one 
figure  variant  most   readily  recognized,  because  it  has  the  normal 
of  katun  sign.  ^-^^  supcrfix,  is  showu  in  figure  29,  d,  e.  The 

determining  characteristic  of  the  head  variant  of  the  tun  glyph, 
however,  is  the  fleshless  lower  jaw  ({),  as  shown  in  figure  29 
/,  g,  though  even  this  is  lacking  in  some  few  cases.  The 
form  shown  in  figure  29,  h,  is  found  at  Palenque,  where  it  ^-j^ 


e  f  g  h 

Fig.  29.   Signs  for  the  tun:  a-d,  Normal  forms;  e-h,  head  variants. 

seems  to  represent  the  tun  period  in  several  places.  The  head  of 
the  full-figure  form  (fig.  30)  has  the  same  fleshless  lower  jaw  for  its 
essential  characteristic  as  the  head-variant  forms  in  fig- 
ure 29.  The  body  joined  to  this  head  is  again  that  of  a 
bird  the  identity  of  which  has  not  yet  been  determined. 

THE  UINAL  GLYPH 

The  period  occupying  the  2d  place  was  called  by  the 
Maya  uinal  or  u.    This  latter  word  means  also  "  the 
Fig.  30.  Full-fig-  moou  "  in  Maya,  and  the  fact  that  the  moon  is  visible 
ure  variant  of  f^^j.  j^gj^  about  20  davs  in  cach  lunation  may  account 

tun  sign.  , 

for  the  application  of  its  name  to  the  20-day  period. 
The  normal  form  of  the  uinal  glyph  in  the  inscriptions  (see  fig.  31, 
a,  h)  is  practically  identical  with  the  form  in  the  codices  (see  fig.  31,  c). 


MORLEY  ] 


INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


71 


/ 

Signs  for  the  uinal:  a-c,  Normal  forms;  d~f,  head 


variants. 


Sometimes  the  subfixial  element         is  omitted  in  the  inscrip- 
tions,  as  in  figure  31,  a.    The  head  variant  of  the  uinal  glyph  (lig.  jj 
31,  d-f)  is  the  most  constant  of  all  of  the  head  forms  for  the  various 
periods.   Its  determining  characteristic  is  the  large  curl  emerging  from 
the  back  part  of  the  mouth.   The  sharp-pointed  teeth  in  the  upper 
jaw  are  also  a  fairly  constant  feature.   In  very  rare  cases  both  of  these 

elements  are  wanting.  In   

such  cases  the  glyph  seems  /  ^=^^\^  f^^^^ 
to  be  without  determining 
characteristics.  The  ani- 
mal represented  in  the  full- 
figure  variants  of  the  uinal 
is  that  of  a  frog  (fig.  32,) 
the  head  of  which  presents 
precisely  the  same  char- 
acteristics as  the  head  vari- 
ants of  the  uinal,  just  de- 
scribed. That  the  head 
variant  of  the  uinal-period 
glyph  was  originally  de- 
rived from  the  representation  of  a  frog  can  hardly  be  denied  in  the 
face  of  such  striking  confirmatory  evidence  as  that  afforded  by  the 
full-figure  form  of  the  uinal  in  figure  33.  Here  the  spotted  body, 
flattened  head,  prominent  mouth,  and  bulging  eyes  of  the  frog  are  so 

reahstically  portrayed  that  there  is  no 
doubt  as  to  the  identity  of  the  figure  in- 
tended. Mr.  Bowditch  (1910:  p.  257)  has 
pointed  out  in  this  connection  an  inter- 
esting phonetic  coincidence,  which  can 
hardly  be  other  than  intentional.  The 
Maya  word  for  frog  is  tto,  which  is  a  fairly  close  phonetic  approxi- 
mation of  u,  the  Maya  word  for  moon "  or  ''month.''  Consequently, 
the  Maya  may  have  selected  the  figure  of  the  frog  on  phonetic  grounds 
to  represent  their  20-day  period.  If  this  point  could  be 
established  it  would  indicate  an  unmistakable  use  of  the 
rebus  form  of  writing  employed  by  the  Aztec.  That  is, 
the  figure  of  a  frog  in  the  uinal-period  glyph  would  not 
recall  the  object  which  it  pictures,  but  the  sound  of  that 
object's  name,  ^to,  approximating  the  sound  of  7/,  which 
in  turn  expressed  the  intended  idea,  namely,  the  20-day 
period.  Mr.  Bowditch  has  suggested  also  that  the  gro- 
tesque birds  which  stand  for  the  cycle,  katun,  and  tun  periods  in 
these  fuU-figure  forms  may  also  have  been  chosen  because  of  the 
phonetic  similarity  of  their  names  to  the  names  of  these  periods. 


Fig.  32.  Full-figure  variant  of  uinal  sign 
on  Zoomorph  B,  Quirigua. 


Fig.  33.  Full- 
figure  variant 
of  uinal  sign 
on  Stela  D,  Co- 
pan. 


72 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


THE   KIN  GLYPH 

The  period  of  the  1st,  or  lowest,  order  was  called  by  the  Maya  lin, 
which  meant  the  ''sun"  and  by  association  the  ''day."  The  kin,  as 
has  been  explained,  was  the  primary  unit  used  by  the  Maya  in  count- 
ing time.  The  normal  form  of  this  period  glyph  in  the  inscriptions 
is  shown  in  figure  34,  a,  which  is  practically  identical  with  the  form 
in  the  codices  (fig.  34,  l).  In  addition  to  the  normal  form  of  the  kin 
sign,  however,  there  are  several  other  forms  representing  this  period 
which  can  not  be  classified  either  as  head  variants  or  full-figure  vari- 
ants, as  in  figure  34,  c,  for  example,  which  bears  no  resemblance  what- 
ever to  the  normal  form  of  the  kin  sign.    It  is  difficult  to  understand 


e  f  9  h 


i  j  h  I 


Fig.  34.    Signs  for  the  kin:  a,  h,  Normal  forms;  c,  d,  miscellaneous;  e-fc,  head  variants. 

how  two  characters  as  dissimilar  as  those  shown  in  a  and  c,  figure  34^ 
could  ever  be  used  to  express  the  same  idea,  particularly  since  there 
seems  to  be  no  element  common  to  both.  Indeed,  so  dissimilar  are 
they  that  one  is  almost  forced  to  believe  that  they  were  derived  from 
two  entirely  distinct  glyphs.  Still  another  and  very  unusual  sign  for 
the  kin  is  shown  in  figure  34,  d;  indeed,  the  writer  recalls  but  two 
places  where  it  occurs:  Stela  1  at  Piedras  Negras,  and  Stela  C  (north 
side)  at  Quirigua.  It  is  composed  of  the  normal  form  of  the  sign  for 
the  day  Ahau  (fig.  16,  inverted  and  a  subfixial  element  which 
varies  in  each  of  the  two  cases.  These  variants  (fig.  34,  c,  d)  are 
found  only  in  the  inscriptions.  The  head  variants  of  the  kin  period 
differ  from  each  other  as  much  as  the  various  normal  forms  above 
\^^=^  O  given.  The  form  shown  in  figure  34,  e,  may  be  readily 
*       t   recognized  by  its  subfixial  element  (*)  and  the  element  (t)> 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


73 


both  of  which  appear  in  the  normal  form,  figure  34,  a.  In  some  cases, 
as  in  figure  34,  f-h,  this  variant  also  has  the  square  irid  and  the 
crooked,  snag-like  teeth  projecting  from  the  front  of  the  mouth. 
Again,  any  one  of  these  features,  or  even  all,  may  be  lacking.  Another 
and  usually  more  grotesque  type  of  head  (fig.  34, 
i,  j)  has  as  its  essential  element  the  banded  head- 
dress. A  very  unusual  head  variant  is  that  shown 
in  figure  34,  li,  the  essential  characteristic  of  which 
seems  to  be  the  crossbones  in  the  eye.  Mr.  Bow- 
ditch  has  included  also  in  his  list  of  kin  signs  the 
form  shown  in  figure  34,  Z,  from  an  inscription  at 
Tikal.  While  this  glyph  in  fact  does  stand  between 
two  dates  which  are  separated  by  one  day  from  each  fig.  35.  Fuu-sgure 
other,  that  is,  6  Eb  0  Pop  and  7  Ben  1  Pop,  the  -'^-^^ 
writer  believes,  nevertheless,  that  only  the  element  {%) — an  es-  (g) 
sential  part  of  the  normal  form  for  the  kin — here  represents  the  t 
period  one  day,  and  that  the  larger  characters  above  and  below  have 
other  meanings.  In  the  fuU-figure  variants  of  the  kin  sign  the  figure 
portrayed  is  that  of  a  human  being  (fig.  35),  the  head  of  which  is 
similar  to  the  one  in  figure  34,  i,  j,  having  the  same  banded  head- 
dress.^ 

This  concludes  the  presentation  of  the  various  forms  which  stand 
for  the  several  periods  of  Table  VIII.  After  an  exhaustive  study  of 
these  as  found  in  Maya  texts  the  writer  has  reached  the  following 
generalizations  concerning  them: 

1.  Prevalence.  The  periods  in  Initial  Series  are  expressed  far  more 
frequently  by  head  variants  than  by  normal  forms.  The  prepon- 
derance of  the  former  over  the  latter  in  all  Initial  Series  known  is  in 
the  proportion  of  about  80  per  cent  of  the  totaP  against  12  per  cent, 
the  periods  in  the  remaining  8  per  cent  being  expressed  by  these  two 
forms  used  side  by  side.  In  other  words,  four-fifths  of  all  the  Initial 
Series  known  have  their  periods  expressed  by  head-variant  glyphs. 

2.  Antiquity.  Head- variant  period  glyphs  seem  to  have  been  used 
very  much  earlier  than  the  normal  forms.  Indeed,  the  first  use  of 
the  former  preceded  the  first  use  of  the  latter  by  about  300  years, 

I  while  in  Initial  Series  normal-form  period  glyphs  do  not  occur  until 
nearly  100  years  later,  or  about  400  years  after  the  first  use  of  head 
variants  for  the  same  purpose. 

3.  Variation.  Throughout  the  range  of  time  covered  by  the  Initial 
Series  the  normal  forms  for  any  given  time-period  differ  but  little 
from  one  another,  all  following  very  closely  one  fixed  type.  Although 


1  The  figure  on  Zoomorph  B  at  Quirigua,  however,  has  a  normal  human  head  without  grotesque  char- 
acteristics. 

2  The  full-figure  glyphs  are  included  with  the  head  variants  in  this  proportion. 


74 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL,  57 


Fig.  36. 


Period  glyphs,  from  widely  separated  sites  and  of  different 
epochs,  showing  persistence  of  essential  elements. 


neany  200  years  apart  in  point  of  time,  the  early  form  of  the  tun  sign 
in  figure  36,  a,  closely  resembles  the  late  form  shown  in  h  of  the  same 
figure,  as  to  its  essentials.  Or  again,  although  375  years  apart,  the 
early  form  of  the  katun  sign  in  figure  36,  c,  is  practically  identical  with 
the  form  in  figure  36,  d.  Instances  of  this  kind  could  be  multiplied 
indefinitely,  but  the  foregoing  are  sufl^cient  to  demonstrate  that  in 
so  far  as  the  normal-form  period  glyphs  are  concerned  but  little  varia- 
tion occurred  from  first  to  last.  Similarly,  it  may  be  said,  the  head 
variants  for  any  given  period,  while  differing  greatly  in  appearance  at 

different  epochs,  re- 
tained, nevertheless, 
the  same  essential 
characteristic  through- 
out. For  example,  al- 
though the  uinal  sign 
in  figure  36,  e,  precedes 
the  one  in  figure  36,/, 
by  some  800  years,  the 
same  essential  element 
— the  large  mouth  curl 
— appears  in  both. 
Again,  although  300 
years  separate  the  cycle  signs  shown  in  g  and  7i,  figure  36,  the  essen- 
tial characteristic  of  the  early  form  (fig.  36,  g),  the  hand,  is  still 
retained  as  the  essential  part  of  the  late  form  (h). 

4.  Derivation.  We  have  seen  that  the  full-figure  glyphs  probably 
show  the  original  life-forms  from  which  the  head  variants  were 
developed.  And  since  from  (2) ,  above,  it  seems  probable  that  the 
head  variants  are  older  than  the  so-called  normal  forms,  we  may 
reasonably  infer  that  the  full-figure  glyphs  represent  the  life-forms 
whose  names  the  Maya  originally  applied  to  their  periods,  and  further 
that  the  first  signs  for  those  periods  were  the  heads  of  these  life-forms. 
This  develops  a  contradiction  in  our  nomenclature,  for  if  the  forms 
which  we  have  called  head  variants  are  the  older  signs  for  the  periods 
and  are  by  far  the  most  prevalent,  they  should  have  been  called  the 
normal  forms  and  not  variants,  and  vice  versa.  However,  the  use  of 
the  term  ''normal  forms"  is  so  general  that  it  would  be  unwise  at 
this  time  to  attempt  to  introduce  any  change  in  nomenclature. 

Secondary  Series 

The  Initial  Series  method  of  recording  dates,  although  absolutely 
accurate,^  was  nevertheless  somewhat  lengthy,  since  in  order  to 
express  a  single  date  by  means  of  it  eight  distinct  glyphs  were 
required,  namely:  (1)  The  Introducing  glyph;  (2)  the  Cycle  glyph; 

1  Any  system  of  counting  time  which  describes  a  date  in  such  a  manner  that  it  can  not  recur,  satisfying 
all  the  necessary  conditions,  for  374,400  years,  must  be  regarded  as  absolutely  accurate  in  so  far  as  the  range 
of  human  life  on  this  planet  is  concerned. 


MORLBT]      IN-TRODXJCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  75 

(3)  the  Katun  glyph;  (4)  the  Tun  glyph;  (5)  the  Uinal  glyph;  (6) 
the  Kin  glyph;  (7)  the  Day  glyph;  (8)  the  Month  glyph.  Moreover, 
its  use  in  any  inscription  which  contained  more  than  one  date  would 
have  resulted  in  needless  repetition.  For  example,  if  all  the  dates 
on  any  given  monument  were  expressed  by  Initial  Series,  every  one 
would  show  the  long  distance  (more  than  3,000  years)  which  sepa- 
rated it  from  the  common  starting  point  of  Maya  chronology.  It 
would  be  just  like  writing  the  legal  holidays  of  the  current  year  in 
this  way:  February  22d,  1913,  A.  D.,  May  30th,  1913,  A.  D.,  July  4th, 
1913,  A.  D.,  December  25th,  1913,  A.  D. ;  or  in  other  words,  repeating 
in  each  case  the  designation  of  time  elapsed  from  the  starting  point 
of  Christian  chronology. 

The  Maya  obviated  this  needless  repetition  by  recording  but  one 
Initial  Series  date  on  a  monument;  ^  and  from  this  date  as  a  new  point 
of  departure  they  proceeded  to  reckon  the  number  of  days  to  the 
next  date  recorded;  from  this  date  the  numbers  of  days  to  the  next; 
and  so  on  throughout  that  inscription.  By  this  device  the  position 
of  any  date  in  the  Long  Count  (its  Initial  Series)  could  be  calculated, 
since  it  could  be  referred  back  to  a  date,  the  Initial  Series  of  which 
was  expressed.  For  example,  the  terminal  day  of  the  Initial  Series 
given  on  page  64  is  7  Akbal  11  Cumhu,  and  its  position  in  the  Long 
Count  is  fixed  by  the  statement  in  cycles,  katuns,  tuns,  etc.,  that 
1,461,463  days  separate  it  from  the  starting  point,  4  Ahau  8  Cumhu. 
Now  let  us  suppose  we  have  the  date  10  Cimi  14  Cumhu,  which  is 
recorded  as  being  3  days  later  than  the  day  7  Akbal  11  Cumhu,^  the 
Initial  Series  of  which  is  known  to  be  1,461,463.  It  is  clear  that  the 
Initial  Series  corresponding  to  the  date  10  Cimi  14  Cumhu,  although 
not  actually  expressed,  will  also  be  known  since  it  must  equal 
1,461,463  (Initial  Series  of  7  Akbal  11  Cumhu)  +  3  (distance  from 
7  Akbal  11  Cumhu  to  10  Cimi  14  Cumhu) ,  or  1,461,466.  Therefore  it 
matters  not  whether  we  count  three  days  forward  from  7  Akbal  11 
Cumhu,  or  whether  we  count  1,461,466  days  forward  from  the  start- 
ing point  of  Maya  chronology,  4  Ahau  8  Cumhu  since  in  each  case  the 
date  reached  will  be  the  same,  namely,  10  Cimi  14  Cumhu.  The 
former  method,  however,  was  used  more  frequently  than  all  of  the 
other  methods  of  recording  dates  combined,  since  it  insured  all  the 
accuracy  of  an  Initial  Series  without  repeating  for  each  date  so  great 
a  number  of  days. 

Thus  having  one  date  on  a  monument  the  Initial  Series  of  which 
was  expressed,  it  was  possible  by  referring  subsequent  dates  to  it,  or 
to  other  dates  which  in  turn  had  been  referred  to  it,  to  fix  accurately 

1  There  are  a  very  few  monuments  which  have  two  Initial  Series  instead  of  one.  So  far  as  the  writer 
knows,  only  six  monuments  in  the  entire  Maya  area  present  this  feature,  namely.  Stelae  F,  D,  E,  and  A 
at  Quirigua,  Stela  17  at  Tikal,  and  Stela  11  at  YaxchUan. 

2  Refer  to  p.  64  and  figure  23.  It  will  be  noted  that  the  third  tooth  (i.  e.  day)  after  the  one  named  7  Akbal 
11  Cmuhu  is  10  Cimi  14  Cumhu. 


76 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL,  57 


the  positions  of  any  number  of  dates  in  the  Long  Count  without  the 
use  of  their  corresponding  Initial  Series.  Dates  thus  recorded  are 
kno^vTi  as  ''secondary  dates/'  and  the  periods  which  express  their 
distances  from  other  dates  of  known  position  in  the  Long  Count, 
as  ''distance  numbers."  A  secondary  date  with  its  corresponding 
distance  number  has  been  designated  a  Secondary  Series.  In  the 
example  above  given  the  distance  number  3  kins  and  the  date  10 
Cimi  14  Cumhu  would  constitute  a  Secondary  Series. 

Here,  then,  in  addition  to  the  Initial  Series  is  a  second  method,  the 
Secondary  Series,  by  means  of  which  the  Maya  recorded  their  dates. 
The  earliest  use  of  a  Secondary  Series  with  which  the  writer  is  familiar 
(that  on  Stela  36  at  Piedras  Negras)  does  not  occur  until  some  280 
years  after  the  first  Initial  Series.  It  seems  to  have  been  a  later 
development,  probably  owing  its  origin  to  the  desire  to  express  more 
than  one  date  on  a  single  monument.  Usually  Secondary  Series  are 
to  be  counted  from  the  dates  next  preceding  them  in  the  inscriptions 
in  which  they  are  found,  though  occasionally  they  are  counted  from 
other  dates  which  may  not  even  be  expressed,  and  which  can  be 
ascertained  only  by  counting  backward  the  distance  number  from 
its  corresponding  terminal  date.  The  accuracy  of  a  Secondary  series 
date  depends  entirely  on  the  fact  that  it  has  been  counted  from  an 
Initial  Series,  or  at  least  from  another  Secondary  series  date,  which 
in  turn  has  been  derived  from  an  Initial  Series.  If  either  of  these 
contingencies  applies  to  any  Secondary  series  date,  it  is  as  accurate 
a  method  of  fixing  a  day  in  the  Long  Count  as  though  its  correspond- 
ing Initial  Series  were  expressed  in  full.  If,  on  the  other  hand,  a  Sec- 
ondary series  date  can  not  be  referred  ultimately  to  an  Initial  Series 
or  to  a  date  the  Initial  Series  of  which  is  known  though  it  may  not  be 
expressed,  such  a  Secondary  series  date  becomes  only  one  of  the 
18,980  dates  of  the  Calendar  Round,  and  will  recur  at  intervals  of 
every  52  years.  In  other  words,  its  position  m  the  Long  Count  will 
be  unknown. 

Calendar-round  Dates 

Dates  of  the  character  just  described  may  be  called  Calendar- 
round  dates,  since  they  are  accurate  only  within  the  Calendar  Round, 
or  range  of  52  years.  While  accurate  enough  for  the  purpose  of  dis- 
tinguishing dates  in  the  course  of  a  single  lifetime,  this  method  breaks 
down  when  used  to  express  dates  covering  a  long  period.  Witness 
the  chaotic  condition  of  Aztec  chronology.  The  Maya  seem  to  have 
realized  the  limitations  of  this  method  of  dating  and  did  not  employ 
it  extensively.  It  was  used  chiefly  at  Yaxchilan  on  the  Usamacintla 
River,  and  for  this  reason  the  chronology  of  that  city  is  very  much 
awry,  and  it  is  difficult  to  assign  its  various  dates  to  their  proper 
positions  in  the  Long  Count. 


MORLET]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  77 


Period-ending  Dates 

The  Maya  made  use  of  still  another  method  of  dating,  which, 
although  not  so  exact  as  the  Initial  Series  or  the  Secondary  Series, 
is,  on  the  other  hand,  far  more  accurate  than  Calendar  round  dating. 
In  this  method  a  date  was  described  as  being  at  the  end  of  some  par- 
ticular period  in  the  Long  Count;  that  is,  closing  a  certain  cycle, 
katun,  or  tun.^  It  is  clear  also  that  in  this  method  only  the  name 
Ahau  out  of  the  20  given  in  Table  I  can  be  recorded,  since  it  alone 
can  stand  at  the  end  of  periods  higher  than  the  kin.  This  is  true, 
since  : 

1.  The  higher  periods,  as  the  uinal,  tun,  katun,  and  cycle  are  exactly 
divisible  by  20  in  every  case  (see  Table  VIII) ,  and — 

2.  They  are  all  counted  from  a  day,  Ahau,  that  is,  4  Aliau  8  Cumhu. 
Consequently,  all  the  periods  of  the  Long  Count,  except  the  kin  or 
primary  unit,  end  with  days  the  name  parts  of  which  are  the  sign 
Ahau. 

This  method  of  recording  dates  always  involves  the  use  of  at  least 
two  factors,  and  usually  three: 

1.  A  particular  period  of  the  Long  Count,  as  Cycle  9,  or  Katun  14, 
etc. 

2.  The  date  which  ends  the  particular  period  recorded,  as  8  Ahau 
13  Ceh,  or  6  Ahau  13  Muan,  the  closing  dates  respectively  of  Cycle  9 
and  Katun  14  of  Cycle  9;  and 

3.  A  glyph  or  element  which  means  '^ending"  or  ''is  ended,"  or 
which  indicates  at  least  that  the  period  to  which  it  is  attached  has 
come  to  its  close. 

The  first  two  of  these  factors  are  absolutely  essential  to  this  method 
of  dating,  while  the  third,  the  so-called  ''ending  sign,"  is  usually, 
though  not  invariably,  present.  The  order  in  which  these  factors 
are  usually  found  is  first  the  date  composed  of  the  day  glyph  and 
month  glyph,  next  the  "ending  sign,"  and  last  the  glyph  of  the  period 
whose  closing  day  has  just  been  recorded.  Very  rarely  the  period 
glyph  and  its  ending  sign  precede  the  date. 

The  ending  glyph  has  three  distinct  variants:  (1)  the  element 
shown  as  the  prefix  or  superfix  in  figure  37,  a-h,  t,  all  of  which  are 
forms  of  the  same  variant;  (2)  the  flattened  grotesque  head  appear- 
ing either  as  the  prefix  or  superfix  in  i,  r,  u,  v  of  the  same  figure;  and 
(3)  the  hand,  which  appears  as  the  main  element  in  the  forms  shown 
in  figure  37,  j-g.  The  two  first  of  these  never  stand  by  themselves 
but  always  modify  some  other  sign.  The  first  (fig.  37,  a-Ti,  t)  is  always 
attached  to  the  sign  of  the  period  whose  end  is  recorded  either  as  a 


1  This  method  of  dating  does  not  seem  to  have  been  used  with  either  uinal  or  kin  period  endings,  probably 
because  of  the  comparative  frequency  with  which  any  given  date  might  occur  at  the  end  of  either  of  these 
two  periods. 


78 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


superfix  (see  fig.  37,  a,  whereby  the  end  of  Cycle  10  is  indicated  ^) ,  or 
as  a  prefix  (see  t,  whereby  the  end  of  Katun  14  is  recorded).  The 
second  form  is  seen  as  a  prefix  in  u,  whereby  the  end  of  Katun  12  is 
recorded,  and  in  i,  whereby  the  end  of  Katun  11  is  shown.  This 
latter  sign  is  found  also  as  a  superfix  in  r. 

The  hand-ending  sign  rarely  appears  as  modifying  period  glyphs, 
although  a  few  examples  of  such  use  have  been  found  (see  fig.  37, 


r  s  t  .  u  V 

Fig.  37.   Ending  signs  and  elements. 


j,  Jc).  This  ending  sign  usually  appears  as  the  main  element  in  a  sepa- 
rate glyph,  which  precedes  the  sign  of  the  period  whose  end  is  recorded 
(see  fig.  37,  l-q).  In  these  cases  the  subordinate  elements  differ 
somewhat,  although  the  element  (*)  appears  as  the  suffix  in  I,  m, 
(^5)  S  ^'  ^'  element  (f)  as  a  postfix  therein,  also  in  o  and  p. 

*  Y  In  a  few  cases  the  hand  is  combined  with  the  other  ending 
signs,  sometimes  with  one  and  sometimes  with  the  other. 


1  In  Chapter  IV  it  will  be  shown  that  two  bars  stand  for  the  number  10.  It  will  be  necessary  to  anticipate 
the  discussion  of  Maya  numerals  there  presented  to  the  extent  of  stating  that  a  bar  represented  5  and  a 
dot  or  ball,  1.  The  varying  combinations  of  these  two  elements  gave  the  values  up  to  20. 


MORLEY]      IITTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


79 


The  use  of  the  hand  as  expressing  the  meaning  ''ending"  is  quite 
natural.  The  Aztec,  we  have  seen,  called  their  52-year  period  the 
xiuhmolpilli,  or  ^^year  bundle."  This  implies  the  concomitant  idea 
of  'Hying  up."  As  a  period  closed,  metaphorically  speaking,  it  was 
^'tied  up"  or  ''bundled  up."  The  Maya  use  of  the  hand  to  express 
the  idea  ''ending"  may  be  a  graphic  representation  of  the  member 
by  means  of  which  this  ''tying  up"  was  effected,  the  clasped  hand 
indicating  the  closed  period. 

This  method  of  describing  a  date  may  be  called  "dating  by  period 
endings."  It  was  far  less  accurate  than  Initial-series  or  Secondary- 
series  dating,  since  a  date  described  as  occurring  at  the  end  of  a  cer- 
tain katun  could  recur  after  an  interval  of  about  18,000  years  in  round 
numbers,  as  against  374,400  years  in  the  other  2  methods.  For  aU 
practical  purposes,  however,  18,000  years  was  as  accurate  as  374,400 
years,  since  it  far  exceeds  the  range  of  time  covered  by  fche  written 
records  of  mankind  the  world  over. 

Period-ending  dates  were  not  used  much,  and,  as  has  been  stated 
above,  they  are  found  only  in  connection  with  the  larger  periods — 
most  frequently  with  the  katun,  next  with  the  cycle,  and  but  very 
rarely  with  the  tun.  Mr.  Bowditch  (U^IO:  pp.  176  et  seq.)  has  re- 
viewed fuUy  the  use  of  ending  signs,  and  students  are  referred  to  his 
work  for  further  information  on  this  subject. 

U  Kahlay  Katunob 

In  addition  to  the  foregoing  methods  of  measuring  time  and  record- 
ing dates,  the  Maya  of  Yucatan  used  still  another,  which,  however, 
was  probably  derived  directly  from  the  application  of  Period-ending 
dating  to  the  Ijong  Count,  and  consequently  introduces  no  new  ele- 
ments. This  has  been  designated  the  Sequence  of  the  Katuns, 
because  in  this  method  the  katun,  or  7,200-day  period,  was  the  unit 
used  for  measuring  the  passage  of  time.  The  Maya  themselves  called 
the  Sequence  of  the  Katuns  u  tzolan  Icatun,  "the  series  of  the  katuns" ; 
or  u  IcaMay  uxocen  Icatunoh,  "the  record  of  the  count  of  the  katuns  " ; 
or  even  more  simply,  u  IcaJilay  Icatunoh,  'Hhe  record  of  the  katuns." 
These  names  accurately  describe  this  system,  which  is  simply  the 
record  of  the  successive  katuns,  comprising  in  the  aggregate  the  range 
of  Maya  chronology. 

Each  katun  of  the  u  kahlay  katunob  was  named  after  the  designa- 
tion of  its  ending  day,  a  practice  derived  no  doubt  from  Period-ending 
dating,  and  the  sequence  of  these  ending  days  represented  passed 
time,  each  ending  day  standing  for  the  katun  of  which  it  was  the 
close.  The  katun,  as  we  have  seen  on  page  77,  always  ended  with 
some  day  Ahau,  consequently  this  day-name  is  the  only  one  of  the 
twenty  which  appears  in  the  u  kahlay  katunob.  In  this  method  the 
katuns  were  distinguished  from  one  another,  not  by  the  positions 


80 


BUREAU  OF  AMEEICAN  ETHNOLOGY 


[BULL.  57 


which  they  occupied  in  the  cycle,  as  Katun  14,  for  example,  but  by 
the  different  days  Ahau  with  which  they  ended,  as  Katun  2  Ahau, 
Katun  13  Ahau,  etc.    See  Table  IX. 

Table  IX.— SEQUENCE  OF  KATUNS  IN  U  KAHLAY  KATUNOB 


Katun 

2  Ahau 

Katun 

8  Ahau 

Katun 

13  Ahau 

Katun 

6  Ahau 

Katun 

11  Ahau 

Katun 

4  Ahau 

Katun 

9  Ahau 

Katun 

2  Ahau 

Katun 

7  Ahau 

Katun 

13  Ahau 

Katun 

5  Ahau 

Katun 

11  Ahau 

Katun 

3  Ahau 

Katun 

9  Ahau 

Katun 

1  Ahau 

Katun 

7  Ahau 

Katun 

12  Ahau 

Katun 

5  Ahau 

Katun 

10  Ahau 

Katun 

3  Ahau,  etc. 

The  peculiar  retrograding  sequence  of  the  numerical  coefficients  in 
Table  IX,  decreasing  by  2  from  katun  to  katun,  as  2,  13,  11,  9,  7, 
5,  3,  1,  12,  etc.,  results  directly  from  the  number  of  days  which  the 
katun  contains.  Since  the  13  possible  numerical  coefficients,  1  to 
13,  inclusive,  succeed  each  other  in  endless  repetition,  1  following 
immediately  after  13,  it  is  clear  that  in  counting  forward  any  given 
number  from  any  given  numerical  coefficient,  the  resulting  numerical 
coefficient  will  not  be  affected  if  we  first  deduct  all  the  13s  possible 
from  the  number  to  be  counted  forward.  The  mathematical  dem- 
onstration of  this  fact  follows.  If  we  count  forward  14  from  any 
given  coefficient,  the  same  coefficient  will  be  reached  as  if  we  had 
counted  forward  but  1.  This  is  true  because,  (1)  there  are  only  13 
numerical  coefficients,  and  (2)  these  follow  each  other  without  inter- 
ruption, 1  following  immediately  after  13;  hence,  when  13  has 
been  reached,  the  next  coefficient  is  1,  not  14;  therefore  13  or  any 
multiple  thereof  may  be  counted  forward  or  backward  from  any  one 
of  the  13  numerical  coefficients  without  changing  its  value.  This 
truth  enables  us  to  formulate  the  following  rule  for  finding  numerical 
coefficients:  Deduct  all  the  multiples  of  13  possible  from  the  number 
to  be  counted  forward,  and  then  count  forward  the  remainder  from 
the  known  coefficient,  subtracting  13  if  the  resulting  number  is  above 
13,  since  13  is  the  highest  possible  number  which  can  be  attached  to 
a  day  sign.  If  we  apply  this  rule  to  the  sequence  of  the  numerical 
coefficients  in  Table  IX,  we  shall  find  that  it  accounts  for  the  retro- 
grading sequence  there  observed.  The  first  katun  in  Table  IX, 
Katun  2  Ahau,  is  named  after  its  ending  day,  2  Ahau.  Now  let  us 
see  whether  the  application  of  this  rule  will  give  us  13  Ahau  as  the 
ending  day  of  the  next  katun.  The  number  to  be  counted  forward 
from  2  Ahau  is  7,200,  the  number  of  days  in  one  katun;  therefore  we 
must  first  deduct  from  7,200  all  the  13s  possible.  7,200  ^  13  =  553^. 
In  other  words,  after  v/e  have  deducted  all  the  13's  possible,  that  is, 


MORLEY]      INTRODUCTIOK  TO  STUDY  OF  MAYA  HIEROGLYPHS  81 

553  of  them,  there  is  a  remainder  of  11.  This  the  rule  says  is  to  be 
added  (or  counted  forward)  from  the  known  coefficient  (in  this  case 
2)  in  order  to  reach  the  resulting  coefficient.  2  +  11  =  13.  Since 
this  number  is  not  above  13,  13  is  not  to  be  deducted  from  it;  there- 
fore the  coefficient  of  the  ending  day  of  the  second  katun  is  13,  as 
shown  in  Table  IX.  Similarly  we  can  prove  that  the  coefficient  of 
the  ending  day  of  the  third  katun  in  Table  IX  will  be  11.  Again,  we 
have  7,200  to  count  forward  from  the  known  coefficient,  in  this  case 
1 3  (the  coefficient  of  the  ending  day  of  the  second  katun) .  But  we  have 
seen  above  that  if  we  deduct  all  the  13s  possible  from  7,200  there  will 
be  a  remainder  of  11;  consequently  this  remainder  11  must  be  added 
to  13,  the  known  coefficient.  13  +  11=24;  but  since  this  number  is 
above  13,  we  must  deduct  13  from  it  in  order  to  find  out  the  resulting 
coefficient.  24  —  13  =  11,  and  11  is  the  coefficient  of  the  ending  day 
of  the  third  katun  in  Table  IX.  By  applying  the  above  rule,  all  of 
the  coefficients  of  the  ending  days  of  the  katuns  could  be  shown  to 
follow  the  sequence  indicated  in  Table  IX.  And  since  the  ending 
days  of  the  katuns  determined  their  names,  this  same  sequence  is  also 
that  of  the  katuns  themselves. 

The  above  table  enables  us  to  establish  a  constant  by  means  of 
which  we  can  always  find  the  name  of  the  next  katim.  Since  7,200 
is  always  the  number  of  days  in  any  katun,  after  deducting  all  the 
13s  possible  the  remainder  will  always  be  11,  which  has  to  be  ^dded 
to  the  known  coefficient  to  find  the  unknown.  But  since  13  has  to 
be  deducted  from  the  resulting  number  when  it  is  above  13,  sub- 
tracting 2  \Yill  always  give  us  exactly  the  same  coefficient  as  adding 
11;  consequently  we  may  formulate  for  determining  the  numerical 
coefficients  of  the  ending  days  of  katuns  the  following  simple  rule: 
Subtract  2  from  the  coefficient  of  the  ending  day  of  the  preceding 
katun  in  every  case.  A  glance  at  Table  IX  will  demonstrate  the 
truth  of  this  rule. 

In  the  names  of  the  katuns  given  in  Table  IX  it  is  noteworthy  that 
the  positions  which  the  ending  days  occupied  in  the  divisions  of  the 
haab,  or  365-day  year,  are  not  mentioned.  For  example,  the  first 
katun  was  not  called  Katun  2  Ahau  8  Zac,  but  simply  Katun  2  Ahau, 
the  month  part  of  the  day,  that  is,  its  position  in  the  year,  was  omitted. 
This  omission  of  the  month  parts  of  the  ending  days  of  the  katuns  in 
the  u  kahlay  katunob  has  rendered  this  method  of  dating  far  less 
accurate  than  any  of  the  others  previously  described  except  Calendar- 
round  Dating.  For  example,  when  a  date  was  recorded  as  falling 
within  a  certain  katun,  as  Katun  2  Ahau,  it  might  occur  anywhere 
within  a  period  of  7,200  days,  or  nearly  20  years,  and  yet  fulfill  the 
given  conditions.  In  other  words,  no  matter  how  accurately  this 
Katun  2  Ahau  itself  might  be  fixed  in  a  long  stretch  of  time,  there 
was  always  the  possibility  of  a  maximum  error  of  about  20  years  in 
43508°— Bull.  57—15  6 


82 


BUREAU  OF  AMEEICAN  ETHNOLOGY 


[BULL.  57 


such  dating,  since  the  statement  of  the  katun  did  not  fix  a  date  any 
closer  than  as  occurring  somewhere  within  a  certain  20-year  period. 
When  greater  accuracy  was  desired  the  particular  tun  in  which  the 
date  occurred  was  also  given,  as  Tun  13  of  Katun  2  Ahau.  This 
fixed  a  date  as  falling  somewhere  within  a  certain  360  days,  which 
was  accurately  fixed  in  a  much  longer  period  of  time.  Very  rarely, 
in  the  case  of  an  extremely  important  event,  the  Calendar-round 
date  was  also  given  as  9  Imix  19  Zip  of  Tun  9  of  Katun  13  Ahau. 
A  date  thus  described  satisfying  all  the  given  conditions  could  not 
recur  until  after  the  lapse  of  at  least  7,000  years.  The  great  major- 
ity of  events,  however,  recorded  by  this  method  are  described  only 
as  occurring  in  some  particular  katun,  as  Katun  2  Ahau,  for  example, 
no  attempt  being  made  to  refer  them  to  any  particular  division  (tun) 
of  this  period.  Such  accuracy  doubtless  was  sufficient  for  recording 
the  events  of  tribal  history,  since  in  no  case  could  an  event  be  more 
than  20  years  out  of  the  way. 

Aside  from  this  initial  error,  the  accuracy  of  this  method  of  dat- 
ing has  been  challenged  on  the  ground  that  since  there  were  only 
thirteen  possible  numerical  coefiicients,  any  given  katun,  as  Katun 
2  Ahau,  for  example,  in  Table  IX  would  recur  in  the  sequence  after 
the  lapse  of  thirteen  katuns,  or  about  256  years,  thus  paving  the  way 
for  much  confusion.  While  admitting  that  every  thirteenth  katun 
in  the  sequence  had  the  same  name  (see  Table  IX),  the  writer 
believes,  nevertheless,  that  when  the  sequence  of  the  katuns  was 
carefully  kept,  and  the  record  of  each  entered  immediately  after  its 
completion,  so  that  there  could  be  no  chance  of  confusing  it  with 
an  earlier  katun  of  the  same  name  in  the  sequence,  accuracy  in  dating 
could  be  secured  for  as  long  a  period  as  the  sequence  remained 
unbroken.  Indeed,  the  u  kahlay  katunob  ^  from  which  the  synopsis 
of  Maya  history  given  in  Chapter  I  was  com.piled,  accurately  fixes 
the  date  of  events,  ignoring  the  possible  initial  inaccuracy  of  20  years, 
within  a  period  of  more  than  1,100  years,  a  remarkable  feat  for  any 
primitive  chronology. 

How  early  this  method  of  recording  dates  was  developed  is  uncer- 
tain. It  has  not  yet  been  found  (surely)  in  the  inscriptions  in  either 
the  south  or  the  north;  on  the  other  hand,  it  is  so  closely  connected  with 
the  Long  Count  and  Period-ending  dating,  which  occurs  repeatedly 
throughout  the  inscriptions,  that  it  seems  as  though  the  u  kahlay 
katunob  must  have  been  developed  while  this  system  was  still  in  use. 

There  should  be  noted  here  a  possible  exception  to  the  above  state- 
ment, namely,  that  the  u  kahlay  katunob  has  not  been  found  in  the 
inscriptions.    Mr.  Bowditch  (1910:  pp.  192  et  seq.)  has  pointed  out 

1  Theu  kahlay  katunob  on  which  the  historical  summary  given  in  Chapter  I  is  based  shows  an  absolutely 
iminterrupted  sequence  of  katuns  for  more  than  1,100  years.  See  Brinton  (1882  b:  pp.  152-164).  It  is  nec- 
essary to  note  here  a  correction  on  p.  153  of  that  work.  Doctor  Brinton  has  omitted  a  Katun  8  Ahau  from 
this  u  kahlay  katunob,  which  is  present  in  the  Berendt  copy,  and  he  has  incorrectly  assigned  the  abandon- 
ment of  Chichcn  Itza  to  the  preceding  katun,  Katun  10  Ahau,  whereas  the  Berendt  copy  shows  this 
event  took  place  during  the  katun  omitted,  Katun  8  Ahau. 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


83 


what  seem  to  be  traces  of  another  method  of  dating.  This  consists  of 
some  day  Ahau  modified  by  one  of  the  two  elements  shown  in  figure 
38  {a-d  and  e-h,  respectively).  In  such  cases  the  month  part  is  some- 
times recorded,  though  as  frequently  the  day  Ahau  stands  by  itself. 
It  is  to  be  noted  that  in  the  great  majority  of  these  cases  the  days 
Ahau  thus  modified  are  the  ending  days  of  katuns,  which  are  either 
expressed  or  at  least  indicated  in  adjacent  glyphs.  In  other  words, 
the  day  Ahau  thus  modified  is  usually  the  ending  day  of  the  next 
even  katun  after  the  last  date  recorded.  The  writer  believes  that 
this  modification  of  certain  days  Ahau  by  either  of  the  two  ele- 
ments shown  in  figure  38  may  indicate  that  such  days  were  the 
katun  ending  days  nearest  to  the  time  when  the  inscriptions  present- 
ing them  were  engraved.    The  snake  variants  shown  in  figure  38, 


To  o1 


Fig. 


g  h 

•knot"  element  as  used  with  day  sign  Ahau,  possibly  indicating  presence  of  the 
u  kahlay  katxinob  in  the  inscriptions. 


a-d,  are  all  from  Palenque;  the  knot  variants  (e-li  of  the  same  figure) 
are  found  at  both  Copan  and  Quirigua. 

It  may  be  objected  that  one  katun  ending  day  in  each  inscription 
is  far  different  from  a  sequence  of  katun  ending  days  as  shown  in 
Table  IX,  and  that  one  katun  ending  day  by  itself  can  not  be  con- 
strued as  an  u  kahlay  katunob,  or  sequence  of  katuns.  The  differ- 
ence here,  however,  is  apparent  rather  than  real,  and  results  from  the 
different  character  of  the  monuments  and  the  native  chronicles.  The 
u  kahlay  katunob  in  Table  IX  is  but  a  part  of  a  much  longer  sequence 
of  katuns,  which  is  shown  in  a  number  of  native  chronicles  written 
shortly  after  the  Spanish  Conquest,  and  which  record  the  events  of 
Maya  history  for  more  than  1,100  years.  They  are  in  fact  chrono- 
logical synopses  of  Maya  history,  and  from  their  very  nature  they 
have  to  do  with  long  periods.  This  is  not  true  of  the  monuments,^ 
which,  as  we  have  seen,  were  probably  set  up  to  mark  the  passage  of 
certain  periods,  not  exceeding  a  katun  in  length  in  any  case.  Conse- 
quently, each  monument  would  have  inscribed  upon  it  only  one  or  two 

1  There  are,  of  course,  a  few  exceptions  to  this  rule— that  is.  there  are  some  monuments  which  indicate 
an  interval  of  more  than  3,000  years  between  the  extreme  dates.  In  such  cases,  however,  this  interval  is 
not  divided  into  katuns,  nor  in  fact  into  any  regularly  recurring  smaller  unit,  with  the  single  exception 
mentioned  in  footnote  1,  p.  84. 


84 


BUREAU  OF  AMEEICAN  ETHNOLOGY 


[BULL.  57 


katun  ending  days  and  the  events  which  were  connected  more  or  less 
closely  with  it.  In  other  words,  the  monuments  were  erected  at  short 
intervals  ^  and  probably  recorded  events  contemporaneous  with  their 
erection,  while  the  u  kahlay  katunob,  on  the  other  hand, were  historical 
summaries  reaching  back  to  a  remote  time.  The  former  were  the  peri- 
odicals of  current  events,  the  latter  histories  of  the  past.  The  former 
in  the  great  majority  of  cases  had  no  concern  with  the  lapse  of  more 
than  one  or  two  katuns,  while  the  latter  measured  centuries  by  the 
repetition  of  the  same  unit.  The  writer  believes  that  from  the  very 
nature  of  the  monuments — markers  of  current  time — no  u  kahlay 
katunob  will  be  found  on  them,  but  that  the  presence  of  the  katun 
ending  days  above  described  indicates  that  the  u  kahlay  katunob  had 
been  developed  while  the  other  system  was  still  in  use.  If  the  fore- 
going be  true,  the  signs  in  figure  38,  a-li,  would  have  this  meaning: 
"On  this  day  came  to  an  end  the  katun  in  which  fall  the  accompany- 
ing dates,''  or  some  similar  significance. 

If  we  exclude  the  foregoing  as  indicating  the  u  kahlay  katunob, 
we  have  but  one  aboriginal  source,  that  is  one  antedating  the  Spanish 
Conquest,  which  probably  records  a  count  of  this  kind.  It  has  been 
stated  (p.  33)  that  the  Codex  Peresianus  probably  treats  in  part  at 
least  of  historical  matter.  The  basis  for  this  assertion  is  that  in  this 
particular  manuscript  an  u  kahlay  katunob  is  seemingly  recorded; 
at  least  there  is  a  sequence  of  the  ending  days  of  katuns  shown, 
exactly  like  the  one  in  Table  IX,  that  is,  13  Ahau,  11  Ahau,  9  Ahau,  etc. 

At  the  time  of  the  Spanish  Conquest  the  Long  Count  seems  to 
have  been  recorded  entirely  by  the  ending  days  of  its  katuns,  that  is, 
by  the  u  kahlay  katunob,  and  the  use  of  Initial-series  dating  seems 
to  have  been  discontinued,  and  perhaps  even  forgotten.  Native  as 
well  as  Spanish  authorities  state  that  at  the  time  of  the  Conquest  the 
Maya  measured  time  by  the  passage  of  the  katuns,  and  no  mention 
is  made  of  any  system  of  dating  which  resembles  in  the  least  the 
Initial  Series  so  prevalent  in  the  southern  and  older  cities.  While  the 
Spanish  authorities  do  not  mention  the  u  kahlay  katimob  as  do  the 
native  writers,  they  state  very  clearly  that  this  was  the  system  used  in 
counting  time.  Says  Bishop  Landa  (1864:  p.  312)  in  this  connection: 
"The  Indians  not  only  had  a  count  by  years  and  days  .  .  .  but  they  had 
a  certain  method  of  counting  time  and  their  affairs  by  ages,  which  they 
made  from  twenty  to  twenty  years  .  .  .  these  they  call  katunes." 
Cogolludo  (1688 :  lib.  iv,  cap.  v,  p.  186)  makes  a  similar  statement :  "They 
count  their  eras  and  ages,  which  they  put  in  their  books  from  twenty 
to  twenty  years  .  .  .  [these]  they  call  katun."  Indeed,  there  can 
be  but  little  doubt  that  the  u  kahlay  katimob  had  entirely  replaced 
the  Initial  Series  in  recording  the  Long  Count  centuries  before  the 
Spanish  Conquest;  and  if  the  latter  method  of  dating  were  known 


1  On  one  monument,  the  tablet  from  the  Temple  of  the  Inscriptions  at  Palenque,  there  seems  to  be 
recorded  a  kind  of  u  kahlay  katunob;  at  least,  there  is  a  sequence  of  ten  consecutive  katuns. 


morley]      IKTEODUCTIOiT  TO  STUDY  01'  MAYA  HIEEOGLYPHS  85 

at  all,  the  knowledge  of  it  came  only  from  half -forgotten  records  the 
understanding  of  which  was  gradually  passing  from  the  minds  of  men. 

It  is  clear  from  the  foregoing  that  an  important  change  in  recording 
the  passage  of  time  took  place  sometime  between  the  epoch  of  the 
great  southern  cities  and  the  much  later  period  when  the  northern  cities 
flourished.  In  the  former,  time  was  reckoned  and  dates  were  recorded 
by  Initial  Series;  in  the  latter,  in  so  far  as  we  can  judge  from  post- 
Conquest  sources,  the  u  kahlay  katunob  and  Calendar-round  dating 
were  the  only  systems  used.  As  to  when  this  change  took  place, 
we  are  not  entirely  in  the  dark.  It  is  certain  that  the  use  of  the 
Initial  Series  extended  to  Yucatan,  since  monuments  presenting  thi^i 
method  of  dating  have  been  found  at  a  few  of  the  northern  cities, 
namely,  at  Chichen  Itza,  Holactun,  and  Tuluum.  On  the  other 
hand,  it  is  equally  certain  that  Initial  Series  could  not  have  been 
used  very  extensively  in  the  north,  since  they  have  been  discovered 
in  only  these  three  cities  in  Yucatan  up  to  the  present  time.  More- 
over, the  latest,  that  is,  the  most  recent  of  these  three,  was  probably 
contemporaneous  with  the  rise  of  the  Triple  Alliance,  a  fairly  early 
event  of  Northern  Maya  history.  Taking  these  two  points  into  con- 
sideration, the  limited  use  of  Initial  Series  in  the  north  and  the  early 
dates  recorded  in  the  few  Initial  Series  known,  it  seems  likely  that 
Initial-series  dating  did  not  long  survive  the  transplanting  of  the 
Maya  civilization  in  Yucatan. 

Why  this  change  came  about  is  uncertain.  It  could  hardly  have 
been  due  to  the  desire  for  greater  accuracy,  since  the  u  kahlay  katunob 
was  far  less  exact  than  Initial-series  dating;  not  only  could  dates 
satisfying  all  given  conditions  recur  much  more  frequently  in  the 
u  kahlay  katunob,  but,  as  generally  used,  this  method  fixed  a  date 
merely  as  occurring  somewhere  within  a  period  of  about  20  years. 

The  writer  believes  the  change  under  consideration  arose  from  a 
very  different  cause;  that  it  was  in  fact  the  result  of  a  tendency 
toward  greater  brevity,  which  was  present  in  the  glyphic  writing 
from  the  very  earliest  times,  and  which  is  to  be  noted  on  some  of  the 
earliest  monuments  that  have  survived  the  ravages  of  the  passing 
centuries.  At  first,  when  but  a  single  date  was  recorded  on  a  monu- 
ment, an  Initial  Series  was  used.  Later,  however,  when  the  need  or 
desire  had  arisen  to  inscribe  more  than  one  date  on  the  same  monument, 
additional  dates  were  not  expressed  as  Initial  Series,  each  of  which, 
as  we  have  seen,  involves  the  use  of  8  glyphs,  but  as  a  Secondary 
Series,  which  for  the  record  of  short  periods  necessitated  the  use  of 
fewer  glyphs  than  were  employed  in  Initial  Series.  It  would  seem 
almost  as  though  Secondary  Series  had  been  invented  to  avoid  the 
use  of  Initial  Series  when  more  than  one  date  had  to  be  recorded  on 
the  same  monument.  But  this  tendency  toward  brevity  in  dating 
did  not  cease  with  the  invention  of  Secondary  Series.  Somewhat 
later,  dating  by  period-endings  was  introduced,  obviating  the  neces- 


86 


BUKEATJ  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


sity  for  the  use  of  even  one  Initial  Series  on  every  monument,  in 
order  that  one  date  might  be  fixed  in  the  Long  Coimt  to  which  the 
others  (Secondary  Series)  could  be  referred.  For  all  practical  pur- 
poses, as  we  have  seen,  Period-ending  dating  was  as  accurate  as 
Initial-series  dating  for  fixing  dates  in  the  Long  Count,  and  its  sub- 
stitution for  Initial-series  dating  resulted  in  a  further  saving  of 
glyphs  and  a  corresponding  economy  of  space.  Still  later,  probably 
after  the  Maya  had  colonized  Yucatan,  the  u  kahlay  katunob,  which 
was  a  direct  apphcation  of  Period-ending  dating  to  the  Long  Count, 
came  into  general  use.  At  this  time  a  rich  history  lay  behind  the 
Maya  people,  and  to  have  recorded  all  of  its  events  by  their  corre- 
sponding Initial  Series  would  have  been  far  too  cumbersome  a  prac- 
tice. The  u  kahlay  katunob  offered  a  convenient  and  facile  method 
by  means  of  which  long  stretches  of  time  could  be  recorded  and  events 
approximately  dated;  that  is,  within  20  years.  This,  together  with 
the  fact  that  the  practice  of  setting  up  dated  period-markers  seems  to 
have  languished  in  the  north,  thus  eliminating  the  greatest  medium 
of  all  for  the  presentation  of  Initial  Series,  probably  gave  rise  to  the 
change  from  the  one  method  of  recording  time  to  the  other. 

This  concludes  the  discussion  of  the  five  methods  by  means  of 
which  the  Maya  reckoned  time  and  recorded  dates:  (1)  Initial-series 
dating;  (2)  Secondary-series  dating;  (3)  Calendar-round  dating; 
(4)  Period-ending  dating;  (5)  Katun-ending  dating,  or  the  u  kahlay 
katunob.  While  apparently  differing  considerably  from  one  another, 
in  reality  all  are  expressions  of  the  same  fundamental  idea,  the  com- 
bination of  the  numbers  13  and  20  (that  is,  260)  with  the  solar  year 
conceived  as  containing  365  days,  and  all  were  recorded  by  the  same 
vigesimal  system  of  numeration ;  that  is : 

1.  All  used  precisely  the  same  dates,  the  18,980  dates  of  the  Cal- 
endar Round; 

2.  All  may  be  reduced  to  the  same  fundamental  unit,  the  day;  and 

3.  All  used  the  same  time  counters,  those  shown  in  Table  VIII. 
In  conclusion,  the  student  is  strongly  urged  constantly  to  bear  in 

mind  two  vital  characteristics  of  Maya  chronology: 

1.  The  absolute  continuity  of  all  sequences  which  had  to  do  with 
the  counting  of  time:  The  13  numerical  coefficients  of  the  day  names, 
the  20  day  names,  the  260  days  of  the  tonalamatl,  the  365  positions 
of  the  haab,  the  18,980  dates  of  the  Calendar  Round,  and  the  kins, 
uinals,  tuns,  katuns,  and  cycles  of  the  vigesimal  system  of  numera- 
tion. When  the  conclusion  of  any  one  of  these  sequences  had  been 
reached,  the  sequence  began  anew  without  the  interruption  or  omis- 
sion of  a  single  unit  and  continued  repeating  itself  for  all  time. 

2.  All  Maya  periods  expressed  not  current  time,  but  passed  time, 
as  in  the  case  of  our  hours,  minutes,  and  seconds. 

On  these  two  facts  rests  the  whole  Maya  conception  of  time. 


Chapter  IV 


MAYA  ARITHMETIC 

The  present  chapter  will  be  devoted  to  the  consideration  of  Maya 
arithmetic  in  its  relation  to  the  calendar.  It  will  be  shown  how  the 
Maya  expressed  their  numbers  and  how  they  used  their  several  time 
periods.  In  short,  their  arithmetical  processes  will  be  explained, 
and  the  calculations  resulting  from  their  application  to  the  calendar 
will  be  set  forth. 

The  Maya  had  two  different  ways  of  writing  their  numerals,^  namely : 
(1)  With  normal  forms,  and  (2)  with  head  variants  ;  that  is,  each  of  the 
numerals  up  to  and  including  19  had  two  distinct  characters  which  stood 
for  it,  just  as  in  the  case  of  the  time  periods  and  more  rarely,  the  days 
and  months.  The  normal  forms  of  the  numerals  may  be  compared  to 
our  Roman  figures,  since  they  are  built  up  by  the  combination  of 
certain  elements  which  had  a  fixed  numerical  value,  like  the  letters 
I,  V,  X,  L,  C,  D,  and  M,  which  in  Roman  notation  stand  for  the 
values  1,  5,  10,  50,  100,  500,  and  1,000,  respectively.  The  head- 
variant  numerals,  on  the  other  hand,  more  closely  resemble  our 
Arabic  figures,  since  there  was  a  special  head  form  for  each  number 
up  to  and  including  13,  just  as  there  are  special  characters  for  the 
first  nine  figures  and  zero  in  Arabic  notation.  Moreover,  this 
parallel  between  our  Arabic  figures  and  the  Maya  head-variant  nu- 
merals extends  to  the  formation  of  the  higher  numbers.  Thus,  the 
Maya  formed  the  head-variant  numerals  for  14,  15,  16,  17,  18,  and 
19  by  applying  the  essential  characteristic  of  the  head  variant  for  10 
to  the  head  variants  for  4,  5,  6,  7,  8,  and  9,  respectively,  just  as  the 
sign  for  10 — that  is,  one  in  the  tens  place  and  zero  in  the  units  place — 
is  used  in  connection  with  the  signs  for  the  first  nine  figures  in  Arabic 
notation  to  form  the  numbers  11  to  19,  inclusive.  Both  of  these 
notations  occur  in  the  inscriptions,  but  with  very  few  exceptions  ^  no 
head-variant  numerals  have  yet  been  found  in  the  codices. 

Bar  and  Dot  Numerals 

The  Maya '  'Roman  numerals  "—that  is,  the  normal-form  numerals, 
up  to  and  including  19 — were  expressed  by  varying  combinations  of 
two  elements,  the  dot  (•),  which  represented  the  numeral,  or  numeri- 
cal value,  1,  and  the  bar,  or  line  (H^BH),  which  represented  the  nu- 
meral, or  numerical  value,  5.    By  various  combinations  of  these  two 


1  The  word  "numeral,"  as  used  here,  has  been  restricted  to  the  first  twenty  numbers,  0  to  19,  inclu- 
sive. 

2  See  p.  96, footnote  1. 


88 


BUBEAU  OF  AMEEICAN  ETHKOLOGY 


[bull.  57 


elements  alone  the  Maya  expressed  all  the  numerals  from  1  to  19,  in- 
clusive. The  normal  forms  of  the  numerals  in  the  codices  are  shown 
in  figure  39,  in  which  one  dot  stands  for  1,  two  dots  for  2,  three  dots 
for  3,  four  dots  for  4,  one  bar  for  5,  one  bar  and  one  dot  for  6,  one  bar 
and  two  dots  for  7,  one  bar  and  three  dots  for  8,  one  bar  and  four  dots 
for  9,  two  bars  for  10,  and  so  on  up  to  three  bars  and  four  dots  for  19. 
The  normal  forms  of  the  numerals  in  the  inscriptions  (see  fig.  40)  are 
identical  with  those  in  the  codices,  excepting  that  they  are  more  elabo- 
rate, the  dots  and  bars  both  taking  on  various  decorations.  Some  of 
the  former  contain  a  concentric  circle  (*)  or  cross-hatch- 
®  Q  ®  (**) ;  some  appear  as  crescents  (f )  or  W  vQ) 
**  tt  t  curls  (If),  more  rarely  as  (J)  or  (J  J).  The  bars  *  + 
show  even  a  greater  variety  of  treatment  (see  fig.  41) .  All  these  deco- 
rations, however,  in 

^  ••••  no  way  affect  the 

numerical  value  of 
the  bar  and  the 
dot,  which  remain  5 
and  1 ,  respectively, 
throughout  the 
Maya  writing.  Such 
embellishments  as 
those  just  described 
are  found  only  in 
the  inscriptions,  and 
their  use  was  proba- 
bly due  to  the  desire  to  make  the  bar  and  dot  serve  a  decorative 
as  well  as  a  numerical  function. 

An  important  exception  to  this  statement  should  be  noted  here  in 
connection  with  the  normal  forms  for  the  numbers  1,  2,  6,  7,  11,  12, 
16,  and  17,  that  is,  all  which  involve  the  use  of  one  or  two  dots  in  their 
composition.^  In  the  inscriptions,  as  we  have  seen  in  Chapter  II, 
every  glyph  was  a  balanced  picture,  exactly  fitting  its  allotted  space, 
even  at  the  cost  of  occasionally  losing  some  of  its  elements.  To  have 
expressed  the  numbers  1,  2,  6,  7,  11,  12,  16,  and  17  as  in  the  codices, 
with  just  the  proper  number  of  bars  and  dots  in  each  case,  would 
have  left  unsightly  gaps  in  the  outhnes  of  the  glyph  blocks  (see  fig. 
42,  a-7i,  where  these  numbers  are  shown  as  the  coefficients  of  the  katun 
sign).  In  a,  c,  e,  and  g  of  the  same  figure  (the  numbers  1,  6,  11,  and 
16,  respectively)  the  single  dot  does  not  fiU  the  space  on  the  left- 
hand  2  side  of  the  bar,  or  bars,  as  the  case  may  be,  and  consequently 

1  In  one  case,  on  the  west  side  of  Stela  E  at  Quirigua,  the  number  14  is  also  shown  with  an  orna- 
mental element  (*).  This  is  very  unusual  and,  so  far  as  the  writer  knows,  is  the  only  example  of 
its  kind.  The  four  dots  in  the  numbers  4,  9, 14,  and  19  never  appear  thus  separated  in  any  other 
text  known. 

^In  the  examples  given  the  numerical  coefficients  are  attached  as  prefixes  to  the  katun  sign.  Fre- 
quently, liowever,  they  occur  as  suporfixes.  In  such  cases,  however,  the  above  observations  apply  equally 
well. 


•  •  •  • 


•  •  •         •  •  •  • 


•  •  •         •  «  • 


Fig.  39.  Normal  forms  of  numerals  1  to  19,  inclusive,  in  the  codices. 


MORLBY]      IKTRODtJCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  89 

the  left-hand  edge  of  the  glyph  block  in  each  case  is  ragged  Simi- 
larly m  h,  d,f,  and  I,  the  numbers  2,  7,  12,  and  17,  respectively,  the 
two  dots  at  the  left  of  the  bar  or  bars  are  too  far  apart  to  fill  in  the 


o 


© 

ONE 


CoXo)  oO 
TWO 


©©©©   OGGO  c 

FOUR 


{pXo)C6)  OOO 

THREE 


FIVE 


SIX 


SEVEN 


EIGHT 


NINE 


ELEVEN 


i 
1 


i 
31 


TEN 


TWELVE 


I 


THIRTEEN 


FOURTEEN 


FIFTEEN 


SIXTEEN  SEVENTEEN  EIGHTEEN 

Fig.  40.   Normal  forms  of  numerals  1  to  19,  inclusive,  in  the  inscriptions. 


i  ] 


NINETEEN 


left-hand  edge  of  the  glyph  blocks  neatly,  and  consequently  in  these 
cases  also  the  eft  edge  is  ragged.  The  Maya  were  quick  to  note  this 
discordant  note  m  glyph  design,  and  in  the  great  majority  of  the 


4 


Fig.  41.   Examples  of  bar  and  dot  numeral  5,  showing  the  ornamentation  which  the  bar  underwent 
without  affecting  its  numerical  value. 

places  where  these  numbers  (1,  2,  6,  7,  11,  12,  16,  and  17)  had  to  be 
recorded,  other  elements  of  a  purely  ornamental  character  were 
introduced  to  fill  the  empty  spaces.  In  figure  43,  a,  c,  e,  g,  the  spaces 
on  each  side  of  the  single  dot  have  been  fiUed  with  ornamental  cres- 


90 


BUBEAtJ  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


cents  about  the  size  of  the  dot,  and  these  give  the  glyph  in  each  case  a 
final  touch  of  balance  and  harmony,  which  is  lacking  without  them. 
In  hj  d,  f,  and  Ti  of  the  same  figure  a  single  crescent  stands  between 
the  two  numerical  dots,  and  this  again  harmoniously  fills  in  the 


0 

Fig.  42.   Examples  showing  the  way  in  which  the  numerals  1,  2,  6,  7,  11,  12, 16,  and  17  are  not  used  with 

period,  day,  or  month  signs. 


glyph  block.  While  the  crescent  (*)  is  the  usual  form  taken 
by  this  purely  decorative  element,  crossed  lines  are 
§  ^  ^  i  found  in  places,  as  in  (f ) ;  or,  again,  a  pair  of  dotted 
^  tt  f  elements  (ff),  as  in  (J).  These  variants,  however,  are 
of  rare  occurrence,  the  common  form  being  the  crescent  shown  in 
figure  43. 

SB  a 

imrii  € 


OU 


€ 
0 


MS 


Fig.  43.   Examples  showing  the  way  in  which  the  numerals  1,  2, 6,  7, 11, 12, 16,  and  17  are  used  with  period, 
day,  or  month  signs.   Note  the  filling  of  the  otherwise  vacant  spaces  with  ornamental  elements. 

The  use  of  these  purely  ornamental  elements,  to  fill  the  empty 
spaces  in  the  normal  forms  of  the  numerals  1,  2,  6,  7,  11,  12,  16,  and 
17,  is  a  fruitful  source  of  error  to  the  student  of  the  inscriptions. 
Slight  weathering  of  an  inscription  is  often  sufficient  to  make  orna- 
mental crescents  look  exactly  Uke  numerical  dots,  and  consequently 
the  numerals  1,  2,  3  are  frequently  mistaken  for  one  another,  as  are 
also  6,  7,  and  8;  11,  12,  and  13;  and  16,  17,  and  18.  The  student 
must  exercise  the  greatest  caution  at  all  times  in  identifying  these 


MORLEY]      INTEODUCTIOK  TO  STUDY  OF  MAYA  HIEROGLYPHS  91 


numerals  in  the  inscriptions,  or  otherwise  he  will  quickly  find  himself 
involved  in  a  tangle  from  which  there  seems  to  be  no  egress.  Proba- 
bly more  errors  in  reading  the  inscriptions  have  been  made 

through  the  incorrect  identification  of  these  numerals  than  • 

through  any  other  one  cause,  and  the  student  is  urged  ■  ■ 

to  be  continually  on  his  guard  if  he  would  avoid  making  ■  ■  ■ 

this  capital  blunder.  ■  ■  ■  ■ 

Although  the  early  Spanish  authorities  make  no  mention  

of  the  fact  that  the  Maya  expressed  their  numbers  by  bars 

and  dots,  native  testimony  is  not  lacking  on  this  point.   ?  

Doctor  Brinton  (1882  b:  p.  48)  gives  this  extract,  accom-  *  * 

panied  by  the  drawing  shown  in  figure  44,  from  a  native  ■  ■  ■ 

writer  of  the  eighteenth  century  who  clearly  describes  this  ^  ^ 

system  of  writing  numbers :   

They  [our  ancestors]  used  [for  numerals  in  their  calendars]  dots  and 

lines  [i.  e,,  bars]  back  of  them;  one  dot  for  one  year,  two  dots  for  two  ■ 

years,  three  dots  for  three  years,  four  dots  for  four,  and  so  on;  in  ad-  ' 

dition  to  these  they  used  a  line;  one  line  meant  five  years,  two  lines  *  * 

meant  ten  years;  if  one  line  and  above  it  one  dot,  six  years;  if  two  ■  ■  ■ 

dots  above  the  line,  seven  years;  if  three  dot^  above,  eight  years;  if  == 

four  dots  above  the  line,  nine;  a  dot  above  two  lines,  eleven;  if  two  Fig. 44.  Nor- 

dots,  twelve;  if  three  dots,  thirteen.  mal  forms 

This  description  is  so  clear,  and  the  values  therein  as-  ftTSr?- 
signed  to  the  several  combinations  of  bars  and  dots  have  ^!,T'^^:.jS 
been  verified  so  extensively  throughout  both  the  inscrip- 
tions and  the  codices,  that  we  are  justified  in  identif3dng 
the  bar  and  dot  as  the  signs  for  five  and  one,  respectively,  wherever 
they  occur,  whether  they  are  found  by  themselves  or  in  varying 
combinations. 

In  the  codices,  as  will  appear  in  Chapter  VI,  the  bar  and  dot 
numerals  were  painted  in  two  colors,  black  and  red.  These  colors 
were  used  to  distinguish  one  set  of  numerals  from  another,  each  of 
which  has  a  different  use.  In  such  cases,  however,  bars  of  one  color 
are  never  used  with  dots  of  the  other  color,  each  number  being  either 
all  red  or  all  black  (see  p.  93,  footnote  1,  for  the  single  exception  to 
this  rule). 

By  the  development  of  a  special  character  to  represent  the  number 
5  the  Maya  had  far  surpassed  the  Aztec  in  the  science  of  mathematics; 
indeed,  the  latter  seem  to  have  had  but  one  numerical  sign,  the  dot, 
and  they  were  obliged  to  resort  to  the  clumsy  makeshift  of  repeating 
this  in  order  to  represent  all  numbers  above  1.  It  is  clearly  seen 
that  such  a  system  of  notation  has  very  definite  limitations,  which 
must  have  seriously  retarded  mathematical  progress  among  the  Aztec. 

In  the  Maya  system  of  numeration,  which  was  vigesimal,  there  was 
no  need  for  a  special  character  to  represent  the  number  20,^  because 

1  Care  should  be  taken  to  distinguish  the  number  or  figure  20  from  any  period  which  contained  20  periods 
of  the  order  next  below  it;  otherwise  the  uinal,  katun,  and  cycle  glyphs  could  all  be  construed  as  signs 
for  20,  since  each  of  these  periods  contains  20  units  of  the  period  next  lower. 


the  Books 
of  Chilan 
Balam. 


92 


BtJREAU  OP  AMERICAN  ETHNOLOGY 


[bull.  57 


(1)  as  we  have  seen  in  Table  VIII,  20  units  of  any  order  (except  the 
2d,  in  which  only  18  were  required)  were  equal  to  1  unit  of  the  order 
next  higher,  and  consequently  20  could  not  be  attached  to  any  period 
glyph,  since  tliis  number  of  periods  (with  the  above  exception)  was 


f  ((**  *  J 

Fig.  45.   Sign  for  20  in  the  codices. 

always  recorded  as  1  period  of  the  order  next  liigher;  and  (2)  although 
there  were  20  positions  in  each  period  except  the  uinal,  as  20  kins  in 
each  uinal,  20  tuns  in  each  katun,  20  katuns  in  each  cycle,  these  posi- 
tions were  numbered  not  from  1  to  20,  but  on  the  contrary  from  0  to 
19,  a  system  which  eliminated  the  need  for  a  character  expressing  20. 

In  spite  of  the  foregoing 
fact,  however,  the  number 
20  has  been  found  in  the 
codices  (see  fig.  45) .  A  pe- 
culiar condition  there,  how- 
ever, accounts  satisfactorily 
for  its  presence.  In  the  cod- 
ices the  sign  for  20  occurs 
only  in  connection  with  to- 
nalamatls,  which,  as  we 
shall  see  later,  were  usually 
portrayed  in  such  a  manner 
that  the  numbers  of  which 
they  were  composed  could 
not  be  presented  from  bot- 
tom to  oop  in  the  usual 
way,  but  had  to  be  written  horizontally  from  left  to  right.  This 
destroyed  the  possibility  of  numeration  by  position,^  according  to 
the  Maya  point  of  view,  and  consequently  some  sign  was  necessary 
which  should  stand  for  20  regardless  of  its  position  or  relation  to 
others.  The  sign  shown  in  figure  45  was  used  for  this  purpose.  It 
has  not  yet  been  found  in  the  inscriptions,  perhaps  because,  as  was 
pointed  out  in  Chapter  II,  the  inscriptions  generally  do  not  appear 
to  treat  of  tonalamatls. 

If  the  Maya  numerical  system  had  no  vital  need  for  a  character  to 
express  the  number  20,  a  sign  to  represent  zero  was  absolutely  indis- 


FiG.  46.   Sign  for  0  in  the  codices. 


1  The  Maya  numbered  by  relative  position  from  bottom  to  top,  as  will  be  presently  explained. 


MORLEi]       IN^TEODUCTIOlSr  TO  STUDY  OF  MAYA  HIEKOGLYPHS  93 


pensable.  Indeed,  any  numerical  system  which  rises  to  a  second 
order  of  units  requires  a  character  which  will  signify,  when  the  need 
arises,  that  no  units  of  a  certain  order  are  inyolved;  as  zero  units  and 
zero  tens,  for  example,  in  writing  100  in  our  own  Arabic  notation. 

The  character  zero  seems  to  have  played  an  important  part  in  Maya 
calculations,  and  signs  for  it  have  been  found  in  both  the  codices  and 
the  inscriptions.  The  form  found  in  the  codices  (fig.  46)  is  lenticu- 
lar; it  presents  an  interior  dec- 
oration which  does  not  follow 
any  fixed  scheme.^  Only  a 
very  few  variants  occur.  The 
last  one  in  figure  46  has  clearly 
as  one  of  its  elements  the  nor- 
mal form  (lenticular).  The 
remaining  two  are  different. 
It  is  noteworthy,  however, 
that  these  last  three  forms  all 
stand  in  the  2d,  or  uinal,  place 
though  whether  this  fact  has 


Fig.  47.   Sign  for  0  in  the  inscriptions. 


in  the  texts  in  which  they  occur, 
influenced  their  variation  is  unknown. 

Both  normal  forms  and  head  variants  for  zero^  as  indeed  for  all 
the  numbers,  have  been  found  in  the  inscriptions.  The  normal 
forms  for  zero  are  shown  in  figure  47.  They  are  common  and  are 
unmistakable.    An  interesting  origin  for  this  sign  has  been  suggested 

byMr.  A.  P.Maudslay.  On       ,  , 

pages  75  and  76  of  the  Co-  ;**--.*''.^  \  '^*•• 

dex  Tro-Cortesiano  2  the  260 
days  of  a  tonalamatl  are 
graphically  represented  as 
forming  the  outline  shown 
in  figure  48,  a.  Half  of  this 
(see  fig.  48,  h)  is  the  sign 
which  stands  for  zero  (com- 
pare with  fig.  47) .  The  train 
of  association  by  which  half 
of  the  graphic  representa- 
tion of  a  tonalamatl  could 
come  to  stand  for  zero  is 
not  clear.  Perhaps  a  of  figure  48  may  have  signified  that  a  complete 
tonalamatl  had  passed  with  no  additional  days.  From  this  the  sign 
may  have  come  to  represent  the  idea  of  completeness  as  apart  from 
the  tonalamatl,  and  finally  the  general  idea  of  completeness  applica- 

1  This  form  of  zero  is  always  red  and  is  used  with  black  bar  and  dot  numerals  as  well  as  with  red  in  the 
codices. 

2  It  is  interesting  to  note  in  this  connection  that  the  Zapotec  made  use  of  the  same  outline  in  graphic 
representations  of  the  tonalamatl.  On  page  1  of  the  Zapotec  Codex  FejervSry-Mayer  an  outline  formed 
by  the  260  days  of  the  tonalamatl  exactly  like  the  one  in  fig.  48,  a,  is  shown. 


Fig.  48.  Figure  showing  possible  derivation  of  the  sign  for  0 
in  the  inscriptions:  a,  Outline  of  the  days  of  the  tonalamatl  as 
represented  graphically  in  the  Codex  Tro-Cortesiano;  b,  half 
of  same  outline,  which  is  also  sign  for  0  shown  in  fig.  47. 


94 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


ble  to  any  period;  for  no  period  could  be  exactly  complete  without  a 
fractional  remainder  unless  all  the  lower  periods  were  wanting;  that 
is,  represented  by  zero.  Whether  this  explains  the  connection  be- 
tween the  outline  of  the  tonalamatl  and  the  zero  sign,  or  whether 
indeed  there  be  any  connection  between  the  two,  is  of.  course  a 
matter  of  conjecture. 

There  is  still  one  more  normal  form  for  zero  not  included  in  the 
examples  given  above,  which  must  be  described.  This  form  (fig.  49), 
which  occurs  throughout  the  inscriptions  and  in  the  Dresden  Codex,^ 
is  chiefly  interesting  because  of  its  highly  specialized  function. 
Indeed,  it  was  used  for  one  purpose  only,  namely,  to  express  the 
first,  or  zero,  position  in  each  of  the  19  divisions  of  the  haab,  or  year, 
and  for  no  other.  In  other  words,  it  denotes  the  positions  0  Pop, 
0  Uo,  0  Zip,  etc.,  which,  as  we  have  seen  (pp.  47,  48),  corresponded 

with  our  first  days  of  the  months. 
The  forms  shown  in  figure  49,  a-6, 
are  from  the  inscriptions  and  those 
in  f-h  from  the  Dresden  Codex. 
They  are  all  similar.  The  general 
outline  of  the  sign  has  suggested 
the  name  ''the  spectacle''  glyph. 
Its  essential  characteristic  seems 
to  be  the  division  into  two  roughly 
circular  parts,  one  above  the 
other,  best  seen  in  the  Dresden 
Codex  forms  (fig.  49,  f-h)  and  a 
roughly  circular  infix  in  each. 
The  lower  infix  is  quite  regular 
in  all  of  the  forms,  being  a  circle  or  ring.  The  upper  infix,  however, 
varies  considerably.  In  figure  49,  a,  h,  this  ring  has  degenerated  into 
a  loop.  In  c  and  d  of  the  same  figure  it  has  become  elaborated  into 
a  head.  A  simpler  form  is  that  in  /  and  g.  Although  comparatively 
rare,  this  glyph  is  so  unusual  in  form  that  it  can  be  readily  recognized. 
Moreover,  if  the  student  will  bear  in  mind  the  two  following  points 
concerning  its  use,  he  will  never  fail  to  identify  it  in  the  inscriptions : 
The  ''spectacle''  sign  (1)  can  be  attached  only  to  the  glyphs  for  the 
19  divisions  of  the  haab,  or  year,  that  is,  the  18  uinals  and  the  xma 
kaba  kin;  in  other  words,  it  is  found  only  with  the  glyphs  shown  in 
figures  19  and  20,  the  signs  for  the  months  in  the  inscriptions  and 
codices,  respectively. 

(2)  It  can  occur  only  in  connection  with  one  of  the  four  day-signs, 
Ik,  Manik,  Eb,  and  Caban  (see  figs.  16,  c,  j,  s,  t,  u,  a' ,  h',  and  17,  c,  d,  7c, 
r,  X,  y,  respectively) ,  since  these  four  alone,  as  appears  in  Table  VII, 
can  occupy  the  0  (zero)  positions  in  the  several  divisions  of  the  haab. 

1  This  form  of  zero  has  been  found  only  in  the  Dresden  Codex.  Its  absence  from  the  other  two  codices 
is  doubtless  due  to  the  fact  that  the  month  glyphs  are  recorded  only  a  very  few  times  in  them— but  once  in 
the  Codex  Tro-Cortesiano  and  three  times  in  the  Codex  Peresianus. 


MORLEY]      INTEODUCTION  TO  STUDY  OF  MAYA  HIEEOGLYPHS 


95 


Examples  of  the  normal-form  numerals  as  used  with  the  day, 
month,  and  period  glyphs  in  both  the  inscriptions  and  the  codices 
are  shown  in  figure  50.    Under  each  is  given  its  meaning  in  English.* 


10  Ahau 


7  Ahau 


Ahau 


1  Ik 


2  Ik 


1  Kan 


13  Manik 


5  Lamat 


2  Cib 


12  Caban 


5  Caban 


5  Eznab 


Kin  8 


Fig.  50.   Examples  of  the  use  of  bar  and  dot  numerals  with  period,  day,  or  month  signs.   The  translation 
of  each  glyph  appears  below  it. 

^  The  student  is  advised  to  familiarize  himself  with  these  forms,  since 
on  his  ability  to  recognize  them  will  largely  depend  his  progress  in 
reading  the  inscriptions.  This  figure  illustrates  the  use  of  all  the 
foregoing  forms  except  the  sign  for  20  in  figure  45  and  the  sign  for 
zero  in  figure  46.  As  these  two  forms  never  occur  with  day,  month, 
or  period  glyphs,  and  as  they  have  been  found  only  in  the  codices, 
examples  showing  their  use  will  not  be  given  until  Chapter  VI  is 
reached,  which  treats  of  the  codices  exclusively. 

1  The  forms  shown  attached  to  these  numerals  are  those  of  the  day  and  month  signs  (see  figs.  16, 17,  and 
19,  20,  respectively),  and  of  the  period  glyphs  (see  figs.  25-35,  inclusive).  Reference  to  these  figures  will 
explain  the  English  translation  in  the  case  of  any  form  which  the  student  may  not  remember. 


96 


BUREAU  OF  AMEEICAIT  ETHNOLOGY 


[BULL.  57 


Head-variant  Numerals 

Let  us  next  turn  to  the  consideration  of  the  Maya  "Arabic  nota- 
tion/' that  is,  the  head-variant  numerals,  which,  Hke  all  other  known 
head  variants,  are  practically  restricted  to  the  inscriptions. ^  It 
should  be  noted  here  before  proceeding  further  that  the  full-figure 
numerals  found  in  connection  with  full-figure  period,  day,  and  month 
glyphs  in  a  few  inscriptions,  have  been  classified  with  the  head- 
variant  numerals.  As  explained  on  page  67,  the  body-parts  of  such 
glyphs  have  no  function  in  determining  their  meanings,  and  it  is  only 
the  head-parts  which  present  in  each  case  the  determining  character- 
istics of  the  form  intended. 

In  the  "head"  notation  each  of  the  numerals,  0,  1,  2,  3,  4,  5,  6,  7,  8, 
9,  10,  11,  12,  13^  is  expressed  by  a  distinctive  type  of  head;  each 
type  has  its  own  essential  characteristic,  by  means  of  which  it  can 
be  distinguished  from  all  of  the  others.  Above  13  and  up  to  but  not 
including  20,  the  head  numerals  are  expressed  by  the  application  of 
the  essential  characteristic  of  the  head  for  10  to  the  heads  for  3  to  9, 
inclusive.  No  head  forms  for  the  numeral  20  have  yet  been  dis- 
covered. 

The  identification  of  these  head- variant  numerals  in  some  cases  is 
not  an  easy  matter,  since  their  determining  characteristics  are  not 
always  presented  clearly.  Moreover,  in  the  case  of  a  few  numerals, 
notably  the  heads  for  2,  11,  and  12,  the  essential  elements  have  not 
yet  been  determined.  Head  forms  for  these  numerals  occur  so  rarely 
in  the  inscriptions  that  the  comparative  data  are  insufficient  to 
enable  us  to  fix  on  any  particular  element  as  the  essential  one. 
Another  difficulty  encountered  in  the  identification  of  head-variant 
numerals  is  the  apparent  irregularity  of  the  forms  in  the  earfier 
inscriptions.  The  essential  elements  of  these  early  head  numerals 
in  some  cases  seem  to  differ  widely  from  those  of  the  later  forms, 
and  consequently  it  is  sometimes  difficult,  indeed  even  impossible,  to 
determine  their  corresponding  numerical  values. 

1  The  following  possible  exceptions,  however,  should  be  noted:  In  the  Codex  Peresianus  the  i-ffrrr^ 
normal  form  of  the  tirn  sign  sometimes  occurs  attached  to  varying  heads,  as  (*).   Whether  these  t!j2Tg 
heads  denote  numerals  is  unknown,  but  the  construction  of  this  glyph  in  such  cases  (a  head  ^"^^ 
attached  to  the  sign  of  a  time  period)  absolutely  parallels  the  use  of  head-variant  numerals  with 
time-period  glyphs  in  the  inscriptions.   A  much  stronger  example  of  the  possible  use  of  head  numerals  with 

period  glyphs  in  the  codices,  however,  is  found  in  the  Dresden  Codex.   Here  the  accompanying 
M  head  (f)  is  almost  surely  that  for  the  number  16,  the  hatchet  eye  denoting  6  and  the  fleshless  lower 
jaw  10.   Compare  (t)  with  fig.  53, /-i,  where  the  head  for  16  is  shown.   The  glyph  (J)  here 
'       shown  is  the  normal  form  for  the  kin  sign.   Compare  fig.  34,  h.   The  meaning  of  these  two  j  tff^ 
forms  would  thus  seem  to  be  16  kins.   In  the  passage  in  which  these  glyphs  occur  the  gl>T)h 
next  preceding  the  head  for  16  is  "8  tuns,"  the  numerical  coefficient  8  being  expressed  by  one  ^ 
bar  and  three  dots.    It  seems  reasonably  clear  here,  therefore,  that  the  form  in  question  is  a  head 
numeral.   However,  these  cases  are  so  very  rare  and  the  context  where  they  occur  is  so  little  understood, 
that  they  have  been  excluded  in  the  general  consideration  of  head- variant  numerals  presented  above. 

2  It  will  appear  presently  that  the  number  13  could  be  expressed  in  two  different  ways:  (1)  by  a 
special  head  meaning  13,  and  (2)  by  the  essential  characteristic  of  the  head  for  10  applied  to  the  headl 
forS  (i.  e.,  }0-j-3=13), 


mTEODUOTIOK  TO  STUDY  OF  MAYA  HIEEOGLYPHS  97 

The  head-variant  numerals  are  shown  in  figures  51  5-?  T„v 
sigHLfyang  1 ;  see  figure  51,  a-e.    The  essential  element  of  this  head's 


FOUR 


w 

SEVEN 


Fig.  51.   Head-variant  numerals  1  to  7,  inclusive. 

its  forehead  ornament,  which,  to  signify  the  number  1,  must  be 
^  composed  of  more  than  one  part  (*),  in  order  to  distinguish  it  ^ 
from  the  forehead  ornament  (**),  which,  as  we  shall  see  pres-  * 
ently,  is  the  essential  element  of  the  head  for  8  (fig  52  a~f) 
Except  for  their  forehead  ornaments  the  heads  for  1  and' 8  are 
ahnost  identical,  and  great  care  must  be  exercised  in  order  to  avoid 
mistaking  one  for  the  other. 
43508°— Bull.  57— J5  7 


98 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


The  head  for  2  (fig.  51,/,  g)  has  been  found  only  twice  in  the  inscrip- 
tions— on  Lintel  2  at  Piedras  Negras  and  on  the  tablet  in  the  Temple 
of  the  Initial  Series  at  Holactun.  The  oval  at  the  top  of  the  head 
seems  to  be  the  only  element  these  two  forms  have  in  common,  and 
the  writer  therefore  accepts  this  element  as  the  essential  character- 


a  b  c  d  e  f 

EIGHT 


g  h  i  j  h  I 

NINE 


is  tic  of  the  head  for  2,  admitting  at  the  same  time  that  the  evidence 
is  insufficient. 

The  head  for  3  is  shown  in  figure  51,  7i,  i.  Its  determining  charac- 
teristic is  the  fillet,  or  headdress. 

The  head  for  4  is  shown  in  figure  51,  j-m.  It  is  to  be  distin- 
^  guished  by  its  large  prominent  eye  and  square  irid  (*)  (probably 

*  eroded  in  Z),  the  snaglike  front  tooth,  and  the  curling  fang 
^  protruding  from  the  back  part  of  the  mouth  (**)  (wanting  in 
**  Zandm). 


MORLEY] 


mTEODUCTIOI.  TO  STUDY  0..  MAYA  HIEROGLYPHS 


99 


The  head  for  5  (fig.  51,  n-s)  is  always  to  be  identified  bv  if^ 
peculiar  headdress(t),  which  is  the  normal  form  of  X  tun  ^ 
sign.  Compare  figure  29,  a,  K  The  same  elemen  ^  Z  ^ 
a  so  m  the  head  for  15  (see  fig.  53,  B-e).  The  head  Vo  5  is  one 
of  the  most  constant  of  all  the  head  numerals. 


FOURTEEN 


c  d 
FIFTEEN 


g  ^  h 

SIXTEEN 


SEVENTEEN 


EIGHTEEN 


NINETEEN 


Fig.  53.   Head- variant  numerals  14  to  19,  inclusive,  and  0. 

The  head  for  6  (fig.  51,  t-v)  is  similarly  unmistakable.  It  is  always 
characterized  by  the  so-called  hatchet  eye  (ff),  which  appears  cpn 
also  m  the  head  for  16  (fig.  53,  /-^).  ^ 

The  head  for  7  (fig.  51,  w)  is  found  only  once  in  the  inscriptions- 
on  the  east  side  of  Stela  D  at  Quirigua.    Its  essential  characteristic 


100 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


the  large  ornamental  scroll  passing  under  the  eye  and  curling  up  in 
front  of  the  forehead  it),  is  better  seen  in  the  head  for  17 
t     (fig.  53,  j^). 

The  head  for  8  is  shown  in  figure  52,  a-f.  It  is  very  similar  to  the 
head  for  1,  as  previously  explained  (compare  figs.  51,  a-e  and  52,  a-f), 
and  is  to  be  distinguished  from  it  only  by  the  character  of  the  fore- 
head ornament,  which  is  composed  of  but  a  single  element  (tt)- 
In  figure  52,  a,  h,  this  takes  the  form  of  a  large  curl.  In  c  of  the  tt 
same  figure  a  flaring  element  is  added  above  the  curl  and  in  d  and  e 
this  element  replaces  the  curl.  In  /  the  tongue  or  tooth  of  a  gro- 
tesque animal  head  forms  the  forehead  ornament.  The  heads  for  18 
(fig.  53,  n-q)  follow  the  first  variants  (fig.  51,  a,  h),  having  the  large 
curl,  except  q,  which  is  similar  to  d  in  having  a  flaring  element  instead. 

The  head  for  9  occurs  more  frequently  than  all  of  the  others  with 
the  exception  of  the  zero  head,  because  the  great  majority  of  aU 
Initial  Series  record  dates  which  fell  after  the  completion  of  Cycle  9, 
but  before  the  completion  of  Cycle  10.  Consequently,  9  is  the  coeffi- 
cient attached  to  the  cycle  glyph  in  •almost  all  Initial  Series.^  The 
head  for  9  is  shown  in  figure  52,  g-l.  It  has  for  its  essential  charac- 
teristic the  dots  on  the  lower  cheek  or  around  the  mouth  (*).  ^ 
Sometimes  these  occur  in  a  circle  or  again  irregularly.  Occa-  * 
sionally,  as  in  j-l,  the  9  head  has  a  beard,  though  this  is  not  a  con- 
stant element  as  are  the  dots,  which  appear  also  in  the  head  for  19. 
Compare  figure  53,  r. 

The  head  for  10  (fig.  52,  m-r)  is  extremely  important  since  its 
essential  element,  the  fleshless  lower  jaw  (*),  stands  for  the 
numerical  value  10,  in  composition  with  the  heads  for  3,  4,  5,  * 
6,  7,  8,  and  9,  to  form  the  heads  for  13,  14,  15,  16,  17,  18,  and  19, 
respectively.  The  10  head  is  clearly  the  fleshless  skull,  having  the 
truncated  nose  and  fleshless  jaws  (see  fig.  52,  m-p).  The  fleshless 
lower  jaw  is  shown  in  profile  in  all  cases  but  one — Zoomorph  B  at 
Quirigua  (see  r  of  the  same  figure).  Here  a  full  front  view  of  a  10 
head  is  shown  in  which  the  fleshless  jaw  extends  clear  across  the 
lower  part  of  the  head,  an  interesting  confirmation  of  the  fact  that 
this  characteristic  is  the  essential  element  of  the  head  for  10. 

The  head  for  11  (fig.  52,  s)  has  been  found  only  once  in  the  inscrip- 
tions, namely,  on  Lintel  2  at  Piedras  Negras;  hence  comparative 
data  are  lacking  for  the  determination  of  its  essential  element.  This 
head  has  no  fleshless  lower  jaw  and  consequently  would  seem,  there- 
fore, not  to  be  built  up  of  the  heads  for  1  and  10. 

Similarly,  the  head  for  12  (fig.  52,  t-v)  has  no  fleshless  lower  jaw,  and 
consequently  can  not  be  composed  of  the  heads  for  10  and  2.  It  is  to 
be  noted,  however,  that  all  three  of  the  faces  are  of  the  same  type, 
even  though  their  essential  characteristic  has  not  yet  been  determined. 


1  For  the  discussion  of  Initial  Series  in  cycles  other  than  Cycle  9,  see  pp.  194-207. 


MORLEY]      INTEODUCTIOIT  TO  STUDY  OF  MAYA  HIEROGLYPHS  101 


The  head  for  13  is  shown  in  figure  52,  w-V .  Only  the  first  of  these 
forms,  w,  however,  is  built  on  the  10  +  3  basis.  Here  we  see  the  char- 
acteristic 3  head  with  its  banded  headdress  or  fillet  (compare  Ti  and 
i,  fig.  51),  to  which  has  been  added  the  essential  element  of  the  10 
head,  the  fleshless  lower  jaw,  the  combination  of  the  two  giving  the 
head  for  13.  The  other  form  for  13  seems  to  be  a  special  character, 
and  not  a  composition  of  the  essential  elements  of  the  heads  for  3  and 
10,  as  in  the  preceding  example.  This  form  of  the  13  head  (fig.  52, 
x-V)  is  grotesque.  It  seems  to  be  characterized  by  its  long  pendulous 
nose  surmounted  by  a  curl  (*),  its  large  bulging  eye  (**),  and  ^  ^ 
^  a  curl  (t)  or  fang  (ft)  protruding  from  the  back  part  *  ** 
t  tt  of  the  mouth.  Occurrences  of  the  first  type — the  composite 
head — are  very  rare,  there  being  only  two  examples  of  this  kind 
known  in  all  the  inscriptions.  The  form  given  in  w  is  from  the  Temple 
of  the  Cross  at  Palenque,  and  the  other  is  on  the  Hieroglyphic  Stair- 
way at  Copan.  The  individual  type,  having  the  pendulous  nose, 
bulging  eye,  and  mouth  curl  is  by  far  the  more  frequent. 

The  head  for  14  (fig.  53,  a)  is  found  but  once — in  the  inscriptions  on 
the  west  side  of  Stela  F  at  Quirigua.  It  has  the  fleshless  lower  jaw 
denoting  10,  while  the  rest  of  the  head  shows  the  characteristics  of 
4 — the  bulging  eye  and  snaglike  tooth  (compare  fig.  51,  /-m).  The 
curl  protruding  from  the  back  part  of  the  mouth  is  wanting  because 
the  whole  lower  part  of  the  4  head  has  been  replaced  by  the  fleshless 
lower  jaw. 

The  head  for  15  (fig.  53,  h-e)  is  composed  of  the  essential  element  of 
the  5  head  (the  tun  sign;  see  fig.  51,  n-s)  and  the  fleshless  lower  jaw 
of  the  head  for  10. 

The  head  for  16  (fig.  53, /-i)  is  characterized  by  the  fleshless  lower 
jaw  and  the  hatchet  eye  of  the  6  head.  Compare  figures  51,  t-v^  and 
52,  m-r,  which  together  form  16  (10  +  6). 

The  head  for  17  (fig.  53,  f-m)  is  composed  of  the  essential  element 
of  the  7  head  (the  scroll  projecting  above  the  nose;  see  fig.  ^l,w)  and 
the  fleshless  lower  jaw  of  the  head  for  10. 

The  head  for  18  (fig.  53,  n-q)  has  the  characteristic  forehead 
ornament  of  the  8  head  (compare  fig.  52,  a-f)  and  the  fleshless  lower 
jaw  denoting  10. 

Only  one  example  (fig.  53,  r)  of  the  19  head  has  been  found  in  the 
inscriptions.  This  occurs  on  the  Temple  of  the  Cross  at  Palenque 
and  seems  to  be  formed  regularly,  both  the  dots  of  the  9  head  and  the 
fleshless  lower  jaw  of  the  10  head  appearing. 

The  head  for  0  (zero),  figure  53,  s-w,  is  always  to  be  distinguished  by 
the  hand  clasping  the  lower  part  of  the  face  (*).    In  this  sign 


for  zero,  the  hand  probably  represents  the  idea  "ending"  or  * 
"closing,"  just  as  it  seems  to  have  done  in  the  ending  signs  used  with 


102 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


Period-ending  dates.  According  to  the  Maya  conception  of  time, 
when  a  period  had  ended  or  closed  it  was  at  zero,  or  at  least  no  new 
period  had  commenced.  Indeed,  the  normal  form  for  zero  in  figure 
47,  the  head  variant  for  zero  in  figure  53,  s-w,  and  the  form  for  zero 
shown  in  figure  54  are  used  interchangeably  in  the  same  inscription 
to  express  the  same  idea — namely,  that  no  periods  thus  modified  are 
involved  in  the  calculations  and  that  consequently  the  end  of  some 
higher  period  is  recorded;  that  is,  no  fractional  parts  of  it  are  present. 

That  the  hand  in  '^ending  signs"  had  exactly  the  same  meaning 
as  the  hand  in  the  head  variants  for^ero  (fig.  53,  s-w)  receives  striking 
corroboration  from  the  rather  unusual  sign  for  zero  shown  in  figure 
54,  to  which  attention  was  called  above.    The  essential  elements  of 


Fig.  54.  A  sign  for  0,  used  also  to  express  the  idea  "ending"  or  "end  of"  in 
Period-ending  dates.  (See  figs.  47  and  53  s-w,  for  forms  used  interchangeably 
in  the  inscriptions  to  express  the  idea  of  0  or  of  completion.) 


this  sign  are  ^  (1)  the  clasped  hand,  identical  with  the  hand  in  the 
head-variant  forms  for  zero,  and  (2)  the  large  element  above  it,  con- 
taining a  curling  infix.  This  latter  element  also  occurs  though  below 
the  clasped  hand,  in  the  ending  signs"  shown  in  figure  37,  Z,  m,  n, 
the  first  two  of  which  accompany  the  closing  date  of  Katun  14,  and 
the  last  the  closing  date  of  Cycle  13.    The  resemblance  of  these  three 

ending  signs"  to  the  last  three  forms  in  figure  54  is  so  close  that  the 
conclusion  is  well-nigh  inevitable  .that  they  represented  one  and  the 
same  idea.  The  writer  is  of  the  opinion  that  this  meaning  of  the 
hand  (ending  or  completion)  will  be  found  to  explain  its  use  through- 
out the  inscriptions. 

In  order  to  familiarize  the  student  with  the  head-variant  numerals, 
their  several  essential  characteristics  have  been  gathered  together  in 
Table  X,  where  they  may  be  readily  consulted.  Examples  covering 
their  use  with  period,  day,  and  month  glyphs  are  given  in  figure  55 
with  the  corresponding  EngUsh  translations  below. 

Head-variant  numerals  do  not  occur  as  frequently  as  the  bar  and 
dot  forms,  and  they  seem  to  have  been  developed  at  a  much  later 
period.  At  least,  the  earliest  Initial  Series  recorded  with  bar  and  dot  ' 
numerals  antedates  by  nearly  two  hundred  years  the  earhest  Initial 
Series  the  numbers  of  which  are  expressed  by  head  variants.  This 
long  priority  in  the  use  of  the  former  would  doubtless  be  considerably 
diminished  if  it  were  possible  to  read  the  earhest  Initial  Series  which 


1  The  subfixial  element  in  the  first  three  forms  of  fig.  54  does  not  seem  to  be  essential,  since  it  is  wanting 
in  the  last. 


MORLEi]      INTKODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  103 


have  head-variant  numerals;  but  that  the  earliest  of  these  latter 
antedate  the  earliest  bar  and  dot  Initial  Series  may  well  be  doubted. 

Table  X.  CHARACTERISTICS  OF  HEAD-VARIANT  NUMERALS  0  TO  19, 

INCLUSIVE 


Forms 

Characteristics 

Head  for  0  

Clasped  hand  across  lower  part  of  face. 

Head  for  1  

Forehead  ornament  composed  of  more  than  one  part. 

Head  for  2  

Oval  ia  upper  part  of  head.  (?) 

Head  for  3  

Banded  headdress  or  fillet. 

Head  for  4  

Bulging  eye  with  square  irid,  snaglike  front  tooth,  curling  fang  from  back  of  mouth. 

Head  for  5  

Normal  form  of  tun  sign  as  headdress. 

Head  for  6  

"Hatchet  eye." 

Head  for  7  

Large  scroll  passing  tander  eye  and  curling  up  in  front  of  forehead. 

Head  for  8  

Forehead  ornament  composed  of  one  part. 

Head  for  9  

Dots  on  lower  cheek  or  around  mouth  and  in  some  cases  beard. 

Head  for  10  

Fleshless  lower  jaw  and  in  some  cases  other  death's-head  characteristics,  trun- 

cated nose,  etc. 

Head  for  11 

Undetermined. 

Head  for  12  

Undetermined;  type  of  head  known,  however. 

Head  for  13  

(a)  Long  pendulous  nose,  bulging  eye,  and  curling  fang  from  back  of  mouth. 

(6)  Head  for  3  with  fleshless  lower  jaw  of  head  for  10. 

Head  for  14  

Head  for  4  with  fleshless  lower  jaw  of  head  for  10. 

Head  for  15  

Head  for  5  with  fleshless  lower  jaw  of  head  for  10. 

Head  for  16  

Head  for  6  with  fleshless  lower  jaw  of  head  for  10. 

Head  for  17  

Head  for  7  with  fleshless  lower  jaw  of  head  for  10. 

Head  for  18  

Head  for  8  with  fleshless  lower  jaw  of  head  for  10. 

Head  for  19  

Head  for  9  with  fleshless  lower  jaw  of  head  for  10. 

Mention  should  be  made  here  of  a  numerical  form  which  can  not 

Bbe  classified  either  as  a  bar  and  dot  numeral  or  a  head  variant. 
This  is  the  thumb  (*),  which  has  a  numerical  value  of  one. 
We  have  seen  in  the  foregoing  pages  the  different  characters  which 
stood  for  the  numerals  0  to  19,  inclusive.  The  next  point  claiming 
our  attention  is,  how  were  the  higher  numbers  written,  numbers 
which  in  the  codices  are  in  excess  of  12,000,000,  and  in  the  inscrip- 
tions, in  excess  of  1,400,000?  In  short,  how  were  numbers  so  large 
expressed  by  the  foregoing  twenty  (0  to  19,  inclusive)  characters? 

The  Maya  expressed  their  higher  numbers  in  two  ways,  in  both  of 
which  the  numbers  rise  by  successive  terms  of  the  same  vigesimal 
system: 

1.  By  using  the  numbers  0  to  19,  inclusive,  as  multipliers  with  the 
several  periods  of  Table  VIII  (reduced  in  each  case  to  units  of  the 
lowest  order)  as  the  multiplicands,  and — 

2.  By  using  the  same  numbers  ^  in  certain  relative  positions,  each  of 
which  had  a  fixed  numerical  value  of  its  own,  Hke  the  positions  to  the 
right  and  left  of  the  decimal  point  in  our  own  numerical  notation. 


1  As  previously  explained,  the  number  20  is  used  only  in  the  codices  and  there  only  in  connection  with 
tonalamatls. 


104 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL,  57 


The  first  of  these  methods  is  rr.rely  found  outside  of  the  inscriptions, 
while  the  second  is  confined  exclusively  to  the  codices.  Moreover, 
althou2:h  the  first  made  use  of  both  normal-form  and  head-variant 


1  Ahau 


Cycle  1 


3  Zip 


Uinal  4 


Katun 


7  Ahau 


Ahau 


Cycle 


Katun  9 


10  Mol 


12  Caban 


Tun  13 


Tun  13 


13  Pop 


Katun  14 


Tun  15 


Kin  16 


Katun  17 


18  Tzec 


Katun  19 


Kin  O 


Cycle  1 


Fig.  55.   Examples  of  the  use  of  head-variant  numerals  with  period,  day,  or  month  signs.   The  translation 

of  each  glyph  appears  below  it. 

numerals,  the  second  could  be  expressed  by  normal  forms  only,  that 
is,  bar  and  dot  numerals.  This  enables  us  to  draw  a  comparison 
between  these  two  forms  of  Maya  numerals : 

Head-variant  numerals  never  occur  independently,  but  are  always 
prefixed  to  some  period,  day,  or  month  sign.  Bar  and  dot  numerals, 
on  the  other  hand,  frequently  stand  by  themselves  in  the  codices 
unattached  to  other  signs.  In  such  cases,  however,  some  sign  was 
to  be  supplied  mentally  with  the  bar  and  dot  numeral. 


morley]     ii^tkoduction"  to  study  of  maya  hieroglyphs  105 
First  Method  of  Numeration 

In  the  first  of  the  above  methods  the  numhers  0  to  19,  inclusive, 
were  expressed  by  multiplying  the  kin  sign  by  the  numerals  ^  0  to  19 


m  n  o  J)  q 

Fig.  56.   Examples  of  the  first  method  of  numeration,  used,  almost  exclusively  in  the  inscriptions. 

in  turn.  Thus,  for  example,  6  days  was  written  as  shown  in  figure 
56,  a,  12  days  as  shown  in  h,  and  17  days  as  shown  in  c  of  the  same 


1  Whether  the  Maya  used  their  numerical  system  in  the  inscriptions  and  codices  for  counting  anything 
besides  time  is  not  known.  As  used  in  the  texts,  the  numbers  occur  only  in  connection  with  calendric 
matters,  at  least  in  so  far  as  they  have  been  deciphered.  It  is  true  many  numbers  are  found  in  both  the 
inscriptions  and  codices  which  are  attached  to  signs  of  unknown  meaning,  and  it  is  possible  that  these 
may  have  nothing  to  do  with  the  calendar.  An  enumeration  of  cities  or  towns,  or  of  tribute  rolls,  for 
example,  may  be  recorded  in  some  of  these  places.  Both  of  these  subjects  are  treated  of  in  the  Aztec 
manuscripts  and  may  well  be  present  in  Maya  texts. 


106 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


figure.  In  other  words,  up  to  and  including  19  the  numbers  were  ex- 
pressed by  prefijcing  the  sign  for  the  number  desired  to  the  kin  sign, 
that  is,  the  sign  for  1  day.^ 

The  numbers  20  to  359,  inclusive,  were  expressed  by  multiplying 
both  the  kin  and'uinal  signs  by  the  numerical  forms  0  to  19,  and  adding 
together  the  resulting  products.  For  example,  the  number  257  was 
written  as  shown  in  figure  56,  d.  We  have  seen  in  Table  VIII  that  1 
uinal  =  20  kins,  consequently  12  uinals  (the  12  being  indicated  by  2  bars 
and  2  dots)  =  240  kins.  However,  as  this  number  falls  short  of  257  by 
17  kins,  it  is  necessary  to  express  these  by  17  kins,  which  are  written 
immediately  below  the  1 2  uinals .  The  sum  of  these  two  products  ==  257 . 
Again,  the  number  300  is  written  as  in  figure  56,  e.  The  15  uinals 
(three  bars  attached  to  the  uinal  sign)  =  15  X  20  =  300  kins,  exactly 
the  number  expressed.  However,  since  no  kins  are  required  to  com- 
plete the  number,  it  is  necessary  to  show  that  none  were  involved, 
and  consequently  0  kins,  or  ^'no  kins"  is  written  immediately  below 
the  15  uinals,  and  300  +  0  =  300.  One  more  example  will  suffice  to 
show  how  the  numbers  20  to  359  were  expressed.  In  figure  56,/,  the 
number  198  is  shown.  The  9  uinals  =  9  X  20  =  180  kins.  But  this 
number  falls  short  of  198  by  18,  which  is  therefore  expressed  by  18 
kins  written  immediately  below  the  9  uinals  :  and  the  sum  of  these 
two  products  is  198,  the  number  to  be  recorded. 

The  numbers  360  to  7,199,  inclusive,  are  indicated  by  multiplying 
the  kin,  uinal,  and  tun  signs  by  the  numerals  0  to  19,  and  adding 
together  the  resulting  products.  For  example,  the  number  360  is 
shown  in  figure  56,  g.  We  have  seen  in  Table  VIII  that  1  tun  =18 
uinals;  but  18  uinals  =  360  kins  (18X20  =  360);  therefore  1  tun 
also  =  360  kins.  However,  in  order  to  show  that  no  uinals  and 
kins  are  involved  in  forming  this  number,  it  is  necessary  to 
record  this  fact,  which  was  done  by  writing  0  uinals  immedi- 
ately below  the  1  tun,  and  0  kins  immediately  below  the  0  uinals. 
The  sum  of  these  three  products  equals  360  (360  +  0  +  0=360). 
Again,  the  number  3,602  is  shown  in  figure  56,  li.  The  10  tuns  = 
10  X  360  =  3,600  kins.  This  talis  short  of  3,602  by  only  2  units  of  the 
first  order  (2  kins),  therefore  no  uinals  are  involved  in  forming  this 
number,  a  fact  which  is  shown  by  the  use  of  0  uinals  between  the  10 
tuns  and  2  kins.  The  sum  of  these  three  products  =  3,602  (3,600  + 
0  +  2).  Again,  in  figure  56,  i,  the  number  7,100  is  recorded.  The 
19  tuns  =  19x360  =  6,840  kins,  which  falls  short  of  7,100  kins  by 
7,100-6,840  =  260  kins.    But  260  kins  =  13  uinals  with  no  kins 

1  The  numerals  and  periods  given  in  fig.  56  are  expressed  by  their  normal  forms  in  every  case,  since  these 
may  be  more  readily  recognized  than  the  corresponding  head  variants,  and  consequently  entail  less  work 
for  the  student.  It  should  be  borne  in  mind,  however,  that  any  bar  and  dot  numeral  or  any  period  in 
fig.  56  could  be  expressed  equally  well  by  its  corresponding  head  form  without  affecting  in  the  least  the 
values  of  the  resulting  numbers. 


MORLEY]      INTRODUCTIOlsr  TO  STUDY  OF  MAYA  HIEROGLYPHS  107 

remaining.  Consequently,  the  sum  of  these  products  equals  7,100 
(6,840  +  260  +  0). 

The  numbers  7,200  to  143,999  were  expressed  by  multiplying  the 
kin,  uinal,  tun,  and  katun  signs  by  the  numerals  0  to  19,  inclusive, 
and  adding  together  the  resulting  products.  For  example,  figure 
56,  j,  shows  the  number  7,204.  We  have  seen  in  Table  VIII  that  1 
katun  =  20  tuns,  and  we  have  seen  that  20  tuns  =  7,200  kins  (20  X  360) ; 
therefore  1  katun  =  7,200  kins.  This  number  falls  short  of  the  num- 
ber recorded  by  exactly  4  kins,  or  in  other  words,  no  tuns  or  uinals 
are  involved  in  its  composition,  a  fact  shown  by  the  0  tuns  and  0 
uinals  between  the  1  katun  and  the  4  kins.  The  sum  of  these  four 
products  =  7,204  (7,200  +  0  +  0  +  4).  The  number  75,550  is  shown  in 
figure  56,  Ic.  The  10  katuns  =  72,000;  the  9  tuns,  3,240;  the  15 
uinals,  300;  and  the  10  kins,  10.  The  sum  of  these  four  products  = 
75,550  (72,000  +  3,240  +  300  +  10).  Again,  the  number  143,567  is 
shown  in  figure  56,  Z.  The  19  katuns=  136,800;  the  18  tuns,  6,480; 
the  14  uinals,  280;  and  the  7  kins,  7.  The  sum  of  these  four  prod- 
ucts =  143,567  (136,800  +  6,480  +  280  +  7) . 

The  numbers  144,000  to  1,872,000  (the  highest  number,  according 
to  some  authorities,  which  has  been  found  ^  in  the  inscriptions)  were 
expressed  by  multiplying  the  kin,  uinal,  tun,  katun,  and  cycle  signs  by 
the  numerals  0  to  19,  inclusive,  and  adding  together  the  resulting 
products.  For  example,  the  number  987,322  is  shown  in  figure  56,  m. 
We  have  seen  in  Table  VIII  that  1  cycle  =  20  katuns,  but  20  ka- 
tuns  =  144,000  kins;  therefore  6  cycles  =  864,000  kins;  and  17 
katuns  =  122,400  kins;  and  2  tuns,  720  kins;  and  10  uinals,  200  kins; 
and  the  2  kins,  2  kins.  The  sum  of  these  five  products  equals  the 
number  recorded,  987,322  (864,000  +  122,400  +  720  +  200  +  2).  The 
highest  number  in  the  inscriptions  upon  which  all  are  agreed  is 
1,872,000,  as  shown  in  figure  56,  n.  It  equals  13  cycles  (13  x  144,000), 
and  consequentl}^  all  the  periods  below — the  katun,  tun,  uinal,  and 
kin — are  indicated  as  being  used  0  times. 


Number  of  Cycles  in  a  Great  Cycle 

This  brings  us  to  the  consideration  of  an  extremely  important  point 
concerning  which  Maya  students  entertain  two  widely  different  opin- 
ions; and  although  its  presentation  will  entail  a  somewhat  lengthy 
digression  from  the  subject  under  consideration  it  is  so  pertinent  to 
the  general  question  of  the  higher  numbers  and  their  formation,  that 
the  writer  has  thought  best  to  discuss  it  at  this  point. 

In  a  vigesimal  system  of  numeration  the  unit  of  increase  is  20,  and 
so  far  as  the  codices  are  concerned,  as  we  shall  presently  see,  this 


1  There  may  be  three  other  numbers  in  the  inscriptions  which  are  considerably  higher  (seepp.  114-127). 


108 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


number  was  in  fact  the  only  unit  of  progression  used,  except  in  the 
2d  order,  in  which  18  instead  of  20  units  were  required  to  make  1 
imit  of  the  3d  order.  In  other  words,  in  the  codices  the  Maya  carried 
out  their  vigesimal  system  to  six  places  without  a  break  other  than 
the  one  in  the  2d  place,  just  noted.    See  Table  VIII. 

In  the  inscriptions,  however,  there  is  some  ground  for  believing 
that  only  13  units  of  the  5th  order  (cycles),  not  20,  were  required  to 
make  1  unit  of  the  6th  order,  or  1  great  cycle.  Both  Mr.  Bowditch 
(1910:  App.  IX,  319-321)  and  Mr.  Goodman  (1897:  p.  25)  incline  to 
this  opinion,  and  the  former,  in  Appendix  IX  of  his  book,  presents 
the  evidence  at  some  length  for  and  against  this  hypothesis. 

This  hypothesis  rests  mainly  on  the  two  following  points : 

1.  That  the  cycles  in  the  inscriptions  are  numbered  from  1  to  13, 
inclusive,  and  not  from  0  to  19,  inclusive,  as  in  the  case  of  all  the 
other  periods  except  the  uinal,  which  is  numbered  from  0  to  17, 
inclusive. 

2.  That  the  only  two  Initial  Series  which  are  not  counted  from  the 
date  4  Ahau  8  Cumlni,  the  starting  point  of  Maya  chronology,  are 
counted  from  a  date  4  Ahau  8  Zotz,  which  is  exactly  13  cycles  in 
advance  of  the  former  date. 

Let  us  examine  the  passages  in  the  inscriptions  upon  which  these 
points  rest.  In  three  places  ^  in  the  inscriptions  the  date  4  Ahau 
8  Cumhu  is  declared  to  have  occurred  at  the  end  of  a  Cycle  13;  that 
is,  in  these  three  places  this  date  is  accompanied  by  an  '^ending  sign" 
and  a  Cycle  13.  In  another  place  in  the  inscriptions,  although  the 
starting  point  4  Ahau  8  Cumhu  is  not  itself  expressed,  the  second 
cycle  thereafter  is  declared  to  have  been  a  Cycle  2,  not  a  Cycle  15, 
as  it  would  have  been  had  the  cycles  been  numbered  from  0  to  19, 
inclusive,  like  all  the  other  periods.^  In  still  another  place  the  ninth 
cycle  after  the  starting  point  (that  is,  the  end  of  a  Cycle  13)  is  not  a 
Cycle  2  in  the  following  great  cycle,  as  would  be  the  case  if  the  cycles 
were  numbered  from  0  to  19,  inclusive,  but  a  Cycle  9,  as  if  the  cycles 
were  numbered  from  1  to  13.  Again,  the  end  of  the  tenth  cycle  after 
the  starting  point  is  recorded  in  several  places,  but  not  as  Cycle  3  of 
the  following  great  cycle,  as  if  the  cycles  were  numbered  from  0  to 
19,  inclusive,  but  as  Cycle  10,  as  would  be  the  case  if  the  cycles  were 
numbered  from  1  to  13.  The  above  examples  leave  little  doubt  that 
the  cycles  were  numbered  from  1  to  13,  inclusive,  and  not  from  0  to  19, 
as  in  the  case  of  the  other  periods.  Thus,  there  can  be  no  question 
concerning  the  truth  of  the  first  of  the  two  above  points  on  which 
this  hypothesis  rests. 


1  These  are:  (1)  The  tablet  from  the  Temple  of  the  Cross  at  Palenque;  (2)  Altar  1  at  Piedras  Negras; 
and  (3)  The  east  side  of  Stela  C  at  Quirigua. 

2  This  case  occurs  on  the  tablet  from  the  Temple  of  the  Foliated  Cross  at  Palenque. 


MORLET]      INTRODUCTION"  TO  STUDY  OF  MAYA  HIEROGLYPHS  109 

But  because  this  is  true  it  does  not  necessarily  follow  that  13  cycles 
made  1  great  cycle.  Before  deciding  this  point  let  us  examine  the 
two  Initial  Series  mentioned  above,  as  not  proceeding  from  the  date 
4  Ahau  8  Cumliu,  but  from  a  date  4  Ahau  8  Zotz,  exactly  13  cycles  in 
advance  of  the  former  date. 

These  are  in  the  Temple  of  the  Cross  at  Paxenque  and  on  the  east 
side  of  Stela  C  at  Quirigua.  In  these  two  cases,  if  the  long  numbers 
expressed  in  terms  of  cycles,  katuns,  tuns,  uinals,  and  kins  are 
reduced  to  kins,  and  counted  forward  from  the  date  4  Ahau  8  Cumhu, 
the  starting  point  of  Maya  chronology,  in  neither  case  will  the 
recorded  terminal  day  of  the  Initial  Series  be  reached;  hence  these 
two  Initial  Series  could  not  have  had  the  day  4  Ahau  8  Cumhu  as 
their  starting  point.  It  may  be  noted  here  that  these  two  Initial 
Series  are  the  only  ones  throughout  the  inscriptions  known  at  the 
present  time  which  are  not  counted  from  the  date  4  Ahau  8  Cumhu.* 
However,  by  counting  hackward  each  of  these  long  numbers  from 
their  respective  terminal  days,  8  Ahau  18  Tzec,  in  the  case  of  the 
Palenque  Initial  Series,  and  4  Ahau  8  Cumhu,  in  the  case  of  the 
Quirigua  Initial  Series,  it  will  be  found  that  both  of  them  proceed 
from  the  same  starting  point,  a  date  4  Ahau  8  Zotz,  exactly  13  cycles 
in  advance  of  the  starting  point  of  Maya  chronology.  Or,  in  other 
words,  the  starting  point  of  all  Maya  Initial  Series  save  two,  was 
exactly  13  cycles  later  than  the  starting  point  of  these  two.  Because 
of  this  fact  and  the  fact  that  the  cycles  were  numbered  from  1  to  13, 
inclusive,  as  shown  above,  Mr.  Bowditch  and  Mr.  Goodman  have 
reached  the  conclusion  that  in  the  inscriptions  only  13  cycles  wqtq 
required  to  make  1  great  cycle. 

It  remains  to  present  the  points  against  this  hypothesis,  which 
seem  to  indicate  that  the  great  cycle  in  the  inscriptions  contained 
the  same  number  of  cycles  (20)  as  in  the  codices: 

1.  In  the  codices  where  six  orders  (great  cycles)  are  recorded  it 
takes  20  of  the  5th  order  (cycles)  to  make  1  of  the  6th  order.  This 
absolute  uniformity  in  a  strict  vigesimal  progression  in  the  codices, 
so  similar  in  other  respects  to  the  inscriptions,  gives  presumptive 
support  at  least  to  the  hypothesis  that  the  6th  order  in  the  inscrip- 
tions was  formed  in  the  same  way. 

2.  The  numerical  system  in  both  the  codices  and  inscriptions  is 
identical  even  to  the  slight  irregularity  in  the  second  place,  where 
only  18  instead  of  20  units  were  required  to  make  1  of  the  third  place. 
It  would  seem  probable,  therefore,  that  had  there  been  any  irregu- 
larity in  the  5th  place  in  the  inscriptions  (for  such  the  use  of  13  in  a 
vigesimal  system  must  be  called),  it  would  have  been  found  also  in 
the  codices. 


1  It  seems  probable  that  the  number  on  the  north  side  of  Stela  C  at  Copan  was  not  counted  from  the 
date  4  Ahau  8  Cumhu.  The  writer  has  not  been  able  to  satisfy  himself,  however,  that  this  number  is  an 
Initial  Series, 


110 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


3.  Moreover,  in  the  inscriptions  themselves  the  cycle  glyph  occurs 
at  least  twice  (see  fig.  57,  a,  h)  with  a  coefficient  greater  than  13,  which 
would  seem  fo  imply  that  more  than  13  cycles  could  be  recorded,  and 
consequently  that  it  required  more  than  13  to  make  1  of  the  period  next 
higher.  The  writer  knows  of  no  place  in  the  inscriptions  where  20 
kins,  18  uinals,  20  tuns,  or  20  katuns  are  recorded,  each  of  these  being 
expressed  as  1  uinal,  1  tun,  1  katun,  and  1  cycle,  respectively.^  There- 
fore, if  13  cycles  had  made  1  great  cycle,  14  cycles  would  not  have 
been  recorded,  as  in  figure  57,  a,  but  as  1  great  cycle  and  1  cycle; 
and  17  cycles  would  not  have  been  recorded,  as  in  h  of  the  same  figure, 
but  as  1  great  cycle  and  4  cycles.  The  fact  that  they  were  not 
recorded  in  this  latter  manner  would  seem  to  indicate,  therefore,  that 

more  than  13  cycles  were  required  to  make 


a 


O       Q  ^  great  cycle,  or  unit  of  the  6tli  place,  in 
the  inscriptions  as  well  as  in  the  codices. 

The  above  points  are  simpiy  positive  evi- 
dence in  support  of  this  hypothesis,  however, 
and  in  no  way  attempt  to  explain  or  other- 
FiG.  57.  Signs  for  thecycieshowing  wisc  accouut  for  the  Undoubtedly  coutra- 

coefficientsabovel3:a,  Fromthe    dictory  poiuts  givCU  in  the  disCUSsioU  of  (1) 

l^enque^'^^om^stl^^^^^^  on  pagcs  108-109.    Furthermore,  not  until 

these  contradictions  have  been  cleared  away 
can  it  be  established  that  the  great  cycle  in  the  inscriptions  was  of 
the  same  length  as  the  great  cycle  in  the  codices.  The  writer 
believes  the  following  explanation  will  satisfactorily  dispose  of  these 
contradictions  and  make  possible  at  the  same  time  the  acceptance  of 
the  theory  that  the  great  cycle  in  the  inscriptions  and  in  the  codices 
was  of  equal  length,  being  composed  in  each  case  of  20  cycles. 

Assuming  for  the  moment  that  there  were  13  cycles  in  a  great 
cycle,  it  is  clear  that  if  tliis  were  the  case  13  cycles  could  never  be 
recorded  in  the  inscriptions,  for  the  reason  that,  being  equal  to  1 
great  cycle,  they  would  have  to  be  recorded  in  terms  of  a  great  cycle. 
This  is  true  because  no  period  in  the  inscriptions  is  ever  expressed, 
so  far  as  now  known,  as  the  full  number  of  the  periods  of  which 
it  was  composed.  For  example,  1  uinal  never  appears  as  20  kins; 
1  tun  is  never  written  as  its  equivalent,  18  uinals;  1  katun  is  never 
recorded  as  20  tuns,  etc.  Consequently,  if  a  great  cycle  composed 
of  13  cycles  had  come  to  its  end  with  the  end  of  a  Cycle  13,  which 
fell  on  a  day  4  Ahau  8  Cumhu,  such  a  Cycle  13  could  never  have  been 
expressed,  since  in  its  place  would  have  been  recorded  the  end  of  the 
great  cycle  which  fell  on  the  same  day.  In  other  words,  if  there  had 
been  13  cycles  in  a  great  cycle,  the  cycles  would  have  been  num- 
bered from  0  to  12,  inclusive,  and  the  last.  Cycle  13,  would  have  been 
recorded  instead  as  completing  some  great  cycle.    It  is  necessary  to 

1  Mr.  Bowditch  (1910:  pp.  41-42)  notes  a  seeming  exception  to  this,  not  in  the  inscription,  however, 
but  in  the  Dresden  Codex,  in  which,  in  a  series  of  numbers  on  pp.  71-73,  the  number  390  is  written  19 
uinals  and  10  kins,  instead  of  1  tun,  1  uinal,  and  10  kins. 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEEOGLYPHS  111 


admit  this  point  or  repudiate  the  numeration  of  all  the  other  periods 
in  the  inscriptions.  The  writer  believesj  therefore,  that,  when  the 
starting  point  of  Maya  chronology  is  declared  to  be  a  date  4  Ahau  8 
Cumhu,  which  an  '^ending  sign"  and  a  Cycle  13  further  declare  fell  at 
the  close  of  a  Cycle  13,  this  does  not  indicate  that  there  were  13 
cycles  in  a  great  cycle,  but  that  it  is  to  be  interpreted  as  a  Period- 
ending  date,  pure  and  simple.  Indeed,  where  this  date  is  found  in 
the  inscriptions  it  occurs  with  a  Cycle  13,  and  an  '^ending  sign" 
which  is  practically  identical  with  other  undoubted  '^ending  signs." 
Moreover,  if  we  interpret  these  places  as  indicating  that  there  were 
only  13  cycles  in  a  great  cycle,  we  have  equal  grounds  for  saying  that 
the  great  cycle  contained  only  10  cycles.  For  example,  on  Zoomorph 
G  at  Quirigua  the  date  7  Ahau  18  Zip  is  accompanied  by  an  '^ending 
sign"  and  Cycle  10,  which  on  this  basis  of  interpretation  would  sig- 
nify that  a  great  cycle  had  only  10  cycles.  Similarly,  it  could  be 
shown  by  such  an  interpretation  that  in  some  cases  a  cycle  had  14 
katuns,  that  is,  where  the  end  of  a  Katun  14  was  recorded,  or  17 
katuns,  where  the  end  of  a  Katun  17  was  recorded.  All  such  places, 
including  the  date  4  Ahau  8  Cumhu,  which  closed  a  Cycle  13  at  the 
starting  point  of  Maya  chronology,  are  only  Period-ending  dates,  the 
writer  believes,  and  have  no  reference  to  the  number  of  periods  which 
any  higher  period  contains  whatsoever.  They  record  merely  the  end 
of  a  particular  period  in  the  Long  Count  as  the  end  of  a  certain  Cycle 
13,  or  a  certain  Cycle  10,  or  a  certain  Katun  14,  or  a  certain  Katun 
17,  as  the  case  may  be,  and  contain  no  reference  to  the  beginning  or 
the  end  of  the  period  next  higher. 

There  can  be  no  doubt,  however,  as  stated  above,  that  the  cycles 
were  numbered  from  I'to  13,  inclusive,  and  then  began  again  with  1. 
This  sequence  strikingly  recalls  that  of  the  numerical  coefficients  of 
the  days,  and  in  the  parallel  which  this  latter  sequence  affords,  the 
writer  believes,  lies  the  true  explanation  of  the  misconception  con- 
cerning the  length  of  the  great  cycle  in  the  inscriptions. 


SEQUENCE 

OF 

TWENTY 

CONSECUTIVE 

DATES 

MONTH  POP 

1  Ik 

0 

Pop 

11  Eb 

10  Pop 

2  Akbal 

1 

Pop 

12  Ben 

11  Pop 

3  Kan 

2 

Pop  . 

13  Ix 

12  Pop 

4  Ch.icch.an 

3 

Pop 

1  Men 

13  Pop 

5  Cimi 

4 

Pop 

2  Cib 

14  Pop 

6  Manik 

5 

Pop 

3  Caban 

15  Pop 

7  Lamat 

6 

Pop 

4  Eznab 

16  Pop 

8  Mnluc 

7 

Pop 

5  Cauac 

17  Pop 

9  Oc 

8 

Pop 

6  Ahau 

18  Pop 

10  Chuen 

9 

Pop 

7  Imix 

19  Pop 

The  numerical  coefficients  of  the  days,  as  we  have  seen,  were  num- 
bered from  1  to  13,  inclusive,  and  then  began  again  with  1.  See 


112 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


Table  XI,  in  which  the  20  days  of  the  month  Pop  are  enumerated. 
Now  it  is  evident  from  this  table  that,  although  the  coefficients  of 
the  days  themselves  do  not  rise  above  13,  the  numbers  showing  the 
positions  of  these  days  in  the  month  continue  up  through  19.  In 
other  words,  two  different  sets  of  numerals  were  used  in  describing 
the  Maya  days:  (1)  The  numerals  1  to  13,  inclusive,  the  coefficients 
of  the  days,  and  an  integral  part  of  their  names;  and  (2)  The  numerals 

0  to  19,  inclusive,  showing  the  positions  of  these  da3^s  in  the  divisions 
of  the  year — the  uinals,  and  the  xma  kaba  kin.  It  is  clear  from  the 
foregoing,  moreover,  that  the  number  of  possible  day  coefficients  (13) 
has  nothing  whatever  to  do  in  determining  the  number  of  days  in 
the  period  next  higher.  That  is,  although  the  coefficients  of  the  days 
are  numbered  from  1  to  13,  inclusive,  it  does  not  necessarily  follow 
that  the  next  higher  period  (the  uinal)  contained  only  13  days. 
Similarly,  the  writer  believes  that  while  the  cycles  were  undoubtedly 
numbered — that  is,  named — ^from  1  to  13,  inclusive,  like  the  coeffi- 
cients of  the  days,  it  took  20  of  them  to  make  a  great  cycle,  just  as  it 
took  20  kins  to  make  a  uinal.  The  two  cases  appear  to  be  parallel. 
Confusion  seems  to  have  arisen  through  mistaking  the  name  of  the 
period  for  its  ^position  in  the  period  next  higher — two  entirely  different 
things,  as  we  have  seen. 

A  somewhat  similar  case  is  that  of  the  katuns  in  the  u  kahlay 
katunob  in  Table  IX.  Assuming  that  a  cycle  commenced  with  the 
first  katun  there  given,  the  name  of  this  katun  is  Katun  2  Ahau, 
although  it  occupied  first  position  in  the  cycle.  Again,  the  name 
of  the  second  katun  in  the  sequence  is  Katun  13  Ahau,  although  it 
occupied  the  second  position  in  the  cycle.  In  other  words,  the  katuns 
of  the  u  kahlay  katunob  were  named  quite  independently  of  their 
position  in  the  period  next  higher  (the  cycle),  and  their  names  do  not 
indicate  the  corresponding  positions  of  the  katun  in  the  period  next 
higher. 

Applying  the  foregoing  explanation  to  those  passages  in  the 
inscriptions  which  show  that  the  enumeration  of  the  cycles  was  from 

1  to  13,  inclusive,  we  may  interpret  them  as  follows:  When  we  ffiid 
the  date  4  Ahau  8  Cumhu  in  the  inscriptions,  accompanied  by  an 
'^ending  sign"  and  a  Cycle  13,  that  Cycle  13,"  even  granting  that 
it  stands  at  the  end  of  some  great  cycle,  does  not  signify  that  there 
were  only  13  cycles  in  the  great  cycle  of  which  it  was  a  part.  On  the 
contrary,  it  records  only  the  end  of  a  particular  Cycle  13,  being  a 
Period-ending  date  pure  and  simple.  Such  passages  no  more  fix  the 
length  of  the  great  cycle  as  containing  13  cycles  than  does  the  coeffi- 
cient 13  of  the  day  name  13  Ix  in  Table  XI  limit  the  number  of  days 
in  a  uinal  to  13,  or,  again,  the  13  of  the  katun  name  13  Ahau  in 
Table  IX  limit  the  number  of  katuns  in  a  cycle  to  13.  This  expla- 
nation not  only  accounts  for  the  use  of  the  14  cycles  or  17  cycles,  as 


MORLEY]      INTRODUCTION"  TO  STUDY  OF  MAYA  HIEROGLYPHS  113 

shown  in  figure  57,  a,  h,  but  also  satisfactorily  provides  for  the  enu- 
meration of  the  cycles  from  1  to  13,  inclusive. 

If  the  date  '^4  Ahau  8  Cumhu  ending  Cycle  13"  be  regarded  as  a 
Period-ending  date,  not  as  indicating  that  the  number  of  cycles  in  a 
great  cycle  was  restricted  to  13,  the  next  question  is — Did  a  great 
cycle  also  come  to  an  end  on  the  date  4  Ahau  8  Cumhu — the  starting 
point  of  Maya  chronology  and  the  closing  date  of  a  Cycle  13  ?  That 
it  did  the  writer  is  firmly  convinced,  although  final  proof  of  the  point 
can  not  be  presented  until  numerical  series  containing  more  than  5 
terms  shall  have  been  considered.  (See  pp.  114-127  for  this  discus- 
sion.) The  following  points,  however,  which  may  be  introduced 
here,  tend  to  prove  this  condition: 

1.  In  the  natural  course  of  affairs  the  Maya  would  have  commenced 
their  chronology  with  the  beginning  of  some  great  cycle,  and  to  have 
done  this  in  the  Maya  system  of  counting  time — that  is,  by  elapsed 
periods — it  was  necessary  to  reckon  from  the  end  of  the  preceding 
great  cycle  as  the  starting  point. 

2.  Moreover,  it  would  seem  as  though  the  natural  cycle  with  which 
to  commence  counting  time  would  be  a  Cycle  1,  and  if  this  were  done 
time  would  have  to  be  counted  from  a  Cycle  13,  since  a  Cycle  1  could 
follow  only  a  Cycle  13. 

On  these  two  probabilities,  together  with  the  discussion  on  pages 
114-127,  the  writer  is  inclined  to  beheve  that  the  Maya  com- 
menced their  chronology  with  the  beginning  of  a  great  cycle,  whose 
first  cycle  was  named  Cycle  1,  which  was  reckoned  from  the  close 
of  a  great  cycle  whose  ending  cycle  was  a  Cycle  13  and  whose  ending 
day  fell  on' the  date  4  Ahau  8  Cumhu. 

The  second  point  (see  p.  108)  on  which  rests  the  hypothesis  of  13 
cycles  to  a  great  cycle"  in  the  inscriptions  admits  of  no  such  plausible 
explanation  as  the  first  point.  Indeed,  it  will  probably  never  be 
known  why  in  two  inscriptions  the  Maya  reckoned  time  from  a  start- 
ing point  different  from  that  used  in  all  the  others,  one,  moreover, 
which  was  13  cycles  in  advance  of  the  other,  or  more  than  5,000  years 
earlier  than  the  beginning  of  their  chronology,  and  more  than  8,000 
years  earlier  than  the  beginning  of  their  historic  period.  That  this 
remoter  starting  point,  4  Ahau  8  Zotz,  from  which  proceed  so  far  as 
known  only  two  inscriptions  throughout  the  whole  Maya  area,  stood 
at  the  end  of  a  great  cycle  the  writer  does  not  believe,  in  view  of 
the  evidence  presented  on  pages  114-127.  On  the  contrary,  the 
material  given  there  tends  to  show  that  although  the  cycle  which 
ended  on  the  day  4  Ahau  8  Zotz  was  also  named  Cycle  13,*  it  was  the 
8th  division  of  the  grand  cycle  which  ended  on  the  day  4  Ahau  8  Cumhu, 

1  That  it  was  a  Cycle  13  is  shown  from  the  fact  that  it  was  just  13  cycles  in  advance  of  Cycle  13  ending 
on  the  date  4  Ahau  8  Cumhu. 

43508°— Bull.  57—15  8 


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BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


the  starting  point  of  Maya  chronology,  and  not  the  closing  division 
of  the  preceding  grand  cycle.  However,  without  attempting  to  settle 
this  question  at  this  time,  the  writer  inclines  to  the  belief,  on  the  basis 
of  the  evidence  at  hand,  that  the  great  cycle  in  the  inscriptions  was  of 
the  same  length  as  in  the  codices,  where  it  is  known  to  have  contained 
20  cycles. 


Let  us  return  to  the  discussion  interrupted  on  page  107,  where  the 
first  method  of  expressing  the  higher  numbers  was  being  explained. 
We  saw  there  how  the  higher  numbers  up  to  and  including  1,872,000 
were  written,  and  the  digression  just  concluded  had  for  its  purpose 
ascertaining  how  the  numbers  above  this  were  expressed;  that  is, 
whether  13  or  20  units  of  the  5th  order  were  equal  to  1  unit  of  the  6th 
order.  It  was  explained  also  that  this  number,  1,872,000,  was  perhaps 
the  highest  which  has  been  found  in  the  inscriptions.  Three  possible 
exceptions,  however,  to  this  statement  should  be  noted  here:  (1)  On 
the  east  side  of  Stela  N  at  Copan  six  periods  are  recorded  (see  fig.  58) ; 
(2)  on  the  west  panel  from  the  Temple  of  the  Inscriptions  at  Palenque 
six  and  probably  seven  periods  occur  (see  fig.  59) ;  and  (3)  on  Stela 
10  at  Tikal  eight  and  perhaps  nine  periods  are  found  (see  fig.  60). 
If  in  any  of  these  cases  all  of  the  periods  belong  to  one  and  the 
same  numerical  series,  the  resulting  numbers  would  be  far  higher  than 
1,872,000.  Indeed,  such  numbers  would  exceed  by  many  millions 
all  others  throughout  the  range  of  Maya  writings,  in  either  the 
codices  or  the  inscriptions. 

Before  presenting  these  three  numbers,  however,  a  distinction 
should  be  drawn  between  them.  The  first  and  second  (figs.  58,  59) 
are  clearly  not  Initial  Series.  Probably  they  are  Secondary  Series, 
although  this  point  can  not  be  established  with  certainty,  since  they 
can  not  be  connected  with  any  known  date  the  position  of  which  is 
definitely  fixed.  The  third  number  (fig.  60),  on  the  other  hand,  is  an 
Initial  Series,  and  the  eight  or  nine  periods  of  which  it  is  composed 
may  fix  the  initial  date  of  Maya  chronology  (4  Ahau  8  Cumhu)  in  a 
much  graDder  chronological  scheme,  as  will  appear  presently. 

The  first  of  these  three  niunbers  (see  fig.  58),  if  all  its  six  periods 
belong  to  the  same  series,  equals  42,908,400.  Although  the  order 
of  the  several  periods  is  just  the  reverse  of  that  in  the  numbers  in 
figure  56,  this  difference  is  unessential,  as  will  shortly  be  explained, 
and  in  no  way  affects  the  value  of  the  number  recorded.  Commencing 
at  the  bottom  of  figure  58  with  the  highest  period  involved  and  read- 
ing up,  A6,i  the  14  great  cycles  =40,320,000  kins  (see  Table  VIII,  in 
which  1  great  cycle  =  2,880,000,  and  consequently  14  =  14  X  2,880,000  = 


1  See  p.  156  and  fig.  66  for  method  of  designating  the  individual  glyphs  in  a  text. 


MORLEvr]      INTRODUCTIOI^^  TO  STUDY  OF  MAYA  HIEROGLYPHS  115 


40,320,000) ;  A5,  the  17  cycles  =2,448,000  kins  (17  X  144,000) ;  A4,  the 
19  katuns- 136,800  kins  (19x7,200);  A3,  the  10  tuns  =  3,600  kins 
(10  X  360) ;  A2,  the  0  uinals,  0  kins;  and  the  0  kins,  0  kins.    The  sum 


Fig.  58.   Part  of  the  inscription  on  Stela  N,  Copan,  showing  a  number  composed  of  six  periods. 
Fig.  59.   Part  of  the  inscription  in  the  Temple  of  the  Inscriptions,  Palenque,  showing  a  number  composed 

of  seven  periods. 

Fig.  60.    Part  of  the  inscription  on  Stela  10,  Tikal  (probably  an  Initial  Series),  showing  a  number  composed 

of  eight  periods. 

of  these  products  =  40,320,000  +  2,448,000  +  136,800  +  3,600  +  0  +  0  = 
42,908,400. 

The  second  of  these  three  numbers  (see  fig.  59),  if  all  of  its  seven 
terms  belong  to  one  and  the  same  number,  equals  455,393,401. 
Commencing  at  the  bottom  as  in  figure  58,  the  first  term  A4,  has  the  co- 
efficient 7.  Since  this  is  the  term  following  the  sixth,  or  great  cycle, 
we  may  call  it  the  great-great  cycle.    But  we  have  seen  that  the 


116 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


great  cycle  =  2,880,000;  therefore  the  great-great  cycle  =  twenty  times 
this  number,  or  57,600,000.  Our  text  shows,  however,  that  seven  of 
these  great-great  cycles  are  used  in  the  number  in  question,  therefore 
our  first  term  =  403,200,000.  The  rest  may  be  reduced  by  means  of 
Table  Villas  follows:  B3, 18  great  cycles  =  51,840,000;  A3,2cycles  = 
288,000;  B2,  9  katuns  =  64,800;  A2,  1  tun  =  360;  Bl,  12  uinals  =  240; 
Bl,  1  kin  =  l.  The  sum  of  these  (403,200,000  +  51,840,000  +  288,000  + 
64,800  +  360  +  240  +  1 )  =  455,393,401 . 

The  third  of  these  numbers  (see  fig.  60),  if  all  of  its  terms  belong  to 
one  and  the  same  number,  equals  1,841,639,800.  Commencing  with 
A2,  this  has  a  coefficient  of  1.  Since  it  immediately  follows  the 
great-great  cycle,  which  we  found  above  consisted  of  57,600,000,  we 
may  assume  that  it  is  the  great-great-great  cycle,  and  that  it  con- 
sisted of  20  great-great  cycles,  or  1,152,000,000.  Since  its  coefficient 
is  only  1,  this  large  number  itself  will  be  the  first  term  in  our  series. 
The  rest  may  readily  be  reduced  as  follows:  A3,  11  great-great 
cycles  =  633,600,000 ;  A4,  19  great  cycles  =  54,720,000 ;  A5,  9  cycles  = 
1,296,000;  A6,  3  katuns  =  21,600;  A7,  6  tuns  =  2,160;  A8,  2  uinals  = 
40;  A9,  0  kins  =  0.i  The  sum  of  these  (1,152,000,000  +  633,600,000  + 
54,720,000  +  1,296,000  +  21,600  +  2, 160  +  40  +  0)  =  1,841,639,800,  the 
highest  number  found  anywhere  in  the  Maya  writings,  equivalent  to 
about  5,000,000  years. 

Whether  these  three  numbers  are  actually  recorded  in  the  inscrip- 
tions under  discussion  depends  solely  on  the  question  whether  or  not 
the  terms  above  the  cycle  in  each  belong  to  one  and  the  same  series. 
If  it  could  be  determined  with  certainty  that  these  higher  periods  in 
each  text  were  all  parts  of  the  same  number,  there  would  be  no  further 
doubt  as  to  the  accuracy  of  the  figures  given  above ;  and  more  impor- 
tant still,  the  17  cycles  of  the  first  number  (see  A5,  fig.  58)  would 
then  prove  conclusively  that  more  than  13  cycles  were  required  to 
make  a  great  cycle  in  the  inscriptions  as  well  as  in  the  codices.  And 
furthermore,  the  14  great  cycles  in  A6,  figure  58,  the  18  in  B3,  figure 
59,  and  the  19  in  A4,  figure  60,  would  also  prove  that  more  than  13 
great  cycles  were  required  to  make  one  of  the  period  next  higher — 
that  is,  the  great-great  cycle.  It  is  needless  to  say  that  this  point 
has  not  been  universally  admitted.  Mr.  Goodman  (1897:  p.  132)  has 
suggested  in  the  case  of  the  Copan  inscription  (fig.  58)  that  only  the 
lowest  four  periods — the  19  katuns,  the  10  tuns,  the  0  uinals,  and  the 
0  kins — A2,  A3,  and  A4,2  here  form  the  number;  and  that  if  this 
number  is  counted  backward  from  the  Initial  Series  of  the  inscription, 
it  will  reach  a  Katun  17  of  the  preceding  cycle.   Finally,  Mr.  Goodman 

1  The  kins  are  missing  from  this  number  (see  A9,  fig.  60).  At  the  maximum,  however,  they  could  in- 
crease this  large  number  only  by  19.   They  have  been  used  here  as  at  0. 

2  As  will  be  explained  presently,  the  kin  sign  is  frequently  omitted  and  its  coefficient  attached  to  the 
uinal  glyph.   See  p.  127. 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  117 

believes  this  Katun  17  is  declared  in  the  glyph  following  the  19  katuns 
(A5);  which  the  writer  identifies  as  17  cycles,  and  consequently 
according  to  the  Goodman  interpretation  the  whole  passage  is  a 
Period-ending  date.  Mr.  Bowditch  (1910:  p.  321)  also  offers  the  same 
interpretation  as  a  possible  reading  of  this  passage.  Even  granting 
the  truth  of  the  above,  this  interpretation  still  leaves  unexplained 
the  lowest  glyph  of  the  number,  which  has  a  coefficient  of  14  (A6). 

The  strongest  proof  that  this  passage  will  not  bear  the  construction 
placed  on  it  by  Mr.  Goodman  is  afforded  by  the  very  glyph  upon  which 
his  reading  depends  for  its  verification,  namely,  the  glyph  which  he 
interprets  Katun  17.  This  glyph  (A5)  bears  no  resemblance  to  the 
katun  sign  standing  immediately  above  it,  but  on  the  contrary  has 
for  its  lower  jaw  the  clasping  hand  (*),  which,  as  we  have  seen,  is 
the  determining  characteristic  of  the  cycle  head.  Indeed,  this  * 
element  is  so  clearly  portrayed  in  the  glyph  in  question  that  its  identi- 
fication as  a  head  variant  for  the  cycle  follows  almost  of  necessity. 
A  comparison  of  this  glyph  with  the  head  variant  of  the  cycle  given  in 
figure  25,  J-/,  shows  that  the  two  forms  are  practically  identical. 
This  correction  deprives  Mr.  Goodman's  reading  of  its  chief  support, 
and  at  the  same  time  increases  the  probability  that  all  the  6  terms 
here  recorded  belong  to  one  and  the  same  number.  That  is,  since 
the  first  five  are  the  kin,  uinal,  tun,  katun,  and  cycle,  respectively,  it 
is  probable  that  the  sixth  and  last,  which  follows  immediatel}^  the 
fifth,  without  a  break  or  interiuption  of  an};  kind,  belongs  to  the 
same  series  also,  in  which  event  this  glyph  would  be  most  likely  to 
represent  the  units  of  the  sixth  order,  or  the  so-called  great  cycles. 

The  passages  in  the  Palenque  and  Tikal  texts  (figs.  59  and  60, 
respectively)  have  never  been  satisfactorily  explained.  In  default  of 
calendric  checks,  as  the  known  distance  between  two  dates,  for 
example,  which  may  be  applied  to  these  three  numbers  to  test  their 
accuracy,  the  writer  knows  of  no  better  check  than  to  study  the  char- 
acteristics of  this  possible  great-cycle  glyph  in  all  three,  and  of  the 
possible  great-great-cycle  glyph  in  the  last  two. 

Passing  over  the  kins,  the  normal  form  of  the  uinal  glyph  appears 
in  figures  58,  A2,  and  59,  Bl  (see  fig.  31,  a,  6),  and  the  head  variant 
in  figure  60,  A8.  (See  fig.  31,  d-f.)  Below  the  uinal  sign  in  A3,  fig- 
ure 58,  and  A2,  figure  59,  and  above  A7,  in  figure  60  the  tuns  are  re- 
corded as  head  variants^  in  all  three  of  which  the  fleshless  lower  jaw, 
the  determining  characteristic  of  the  tun  head,  appears.  Compare 
these  three  head  variants  with  the  head  variant  for  the  tun  in  figure  29, 
d-g.  In  the  Copan  inscription  (fig.  58)  the  katun  glyph,  A4,  appears 
as  a  head  variant,  the  essential  elements  of  which  seem  to  be  the  oval 
in  the  top  part  of  the  head  and  the  curling  fang  protruding  from  the 
back  part  of  the  mouth.  Compare  this  head  with  the  head  variant 
for  the  katun  in  figure  27,  e-^.    In  the  Palenque  and  Tikal  texts  (see 


118 


BUREAU  OF  AMERICAN"  ETHNOLOGY 


[BULL.  57 


figs.  59,  B2,  and  60,  A6,  respectively),  on  the  other  hand,  the  katun 
is  expressed  by  its  normal  form,  which  is  identical  with  the  normal 
form  shown  in  figure  27,  a,  h.  In  figures  58,  A5,  and  59,  A3,  the  cycle 
is  expressed  by  its  head  variant,  and  the  determining  characteristic, 
the  clasped  hand,  appears  in  both.  Compare  the  cycle  signs  in  figures 
58,  A5,  and  59,  A3,  with  the  head  variant  for  the  cycle  shown  in 
figure  25,  d-f.  The  cycle  glyph  in  the  Tikal  text  (fig.  60,  A5)  is 
clearly  the  normal  form.  (See  fig.  25,  a-c.)  The  glyph  following  the 
cycle  sign  in  these  three  texts  (standing  above  the  cycle  sign  in  figure 
60  at  A4)  probably  stands  for  the  period  of  the  sixth  order,  the 
so-called  great  cycle.  These  three  glyphs  are  redrawn  in  figure 
61,  a-c,  respectively.  In  the  Copan  inscription  this  glyph  (fig. 
61,  a)  is  a  head  variant,  while  in  the  Palenque  and  Tikal  texts  (a 
and  h   of  the  same  figure,  respectively)  it  is  a  normal  form. 


a  b  c  d  e 

Fig.  61.   Signs  for  the  great  cycle  (a-c),  and  the  great-great  cycle  (d,  e):  a,  Stela  N,  Copan;  b,  d,  Temple 
of  the  Inscriptions,  Palenque;  c,  c,  Stela  10,  Tikal. 

Inasmuch  as  these  three  inscriptions  are  the  only  ones  in  which 
numerical  series  composed  of  6  or  more  consecutive  terms  are 
recorded,  it  is  unfortunate  that  the  sixth  term  in  all  three  should 
not  have  been  expressed  by  the  same  form,  since  this  would  have 
facilitated  their  comparison.  Notwithstanding  this  handicap,  how- 
ever, the  writer  believes  it  will  be  possible  to  show  clearly  that 
the  head  variant  in  figure  61,  a,  and  the  normal  forms  in  h  and  c  are 
only  variants  of  one  and  the  same  sign,  and  that  all  three  stand  for 
one  and  the  same  thing,  namely,  the  great  cycle,  or  unit  of  the  sixth 
order. 

In  the  first  place,  it  will  be  noted  that  each  of  the  three  glyphs  just 
mentioned  is  composed  in  part  of  the  cycle  sign.  For  example,  in 
figure  61,  a,  the  head  variant  has  the  same  clasped  hand  as  the  head- 
variant  cycle  sign  in  the  same  text  (see  fig.  58,  A5),  which,  as 
we  have  seen  elsewhere,  is  the  determining  characteristic  of  the  head 
variant  for  the  cycle.  In  figure  61,  6,  c,  the  normal  forms  there 
presented  contain  the  entire  normal  form  for  the  cycle  sign;  compare 
figure  25,  a,  c.  Indeed,  except  for  its  superfix,  the  glyphs  in  figure  61,5, 
c,  are  normal  forms  of  the  cycle  sign ;  and  the  glyph  in  a  of  the  same 
figure,  except  for  its  superfixial  element,  is  similarly  the  head  variant 
for  the  cycle.  It  would  seem,  therefore,  that  the  determining  charac- 
teristics of  these  three  glyphs  must  be  their  superfixial  elements.  In 
the  normal  form  in  figure  61,  h,  the  superfix  is  very  clear.  Just 
inside  the  outline  and  parallel  to  it  there  is  a  line  of  smaller  circles, 


MORLEY]      INTRODUCTION  TO  STUDY  OP  MAYA  HIEROGLYPHS  119 

and  in  the  middle  there  are  two  infixes  Hke  shepherds'  crooks  facing 
away  from  the  center  (*).  In  c  of  the  last-mentioned  figure  the 
superfix  is  of  the  same  size  and  shape,  and  although  it  is  partially  * 
destroyed  the  left-hand  '^shepherd's  crook"  can  still  be  distinguished. 
A  faint  dot  treatment  around  the  edge  can  also  still  be  traced. 
Although  the  superfix  of  the  head  variant  in  a  is  somewhat  weathered, 
enough  remains  to  show  that  it  was  similar  to,  if  indeed  not  identical 
with,  the  superfixes  of  the  normal  forms  in  h  and  c.  The  line  of  circles 
defining  the  left  side  of  this  superfix,  as  well  as  traces  of  the  lower 
ends  of  the  two  ' 'shepherd's  crook"  infixes,  appears  very  clearly  in 
the  lower  part  of  the  superfix.  Moreover,  in  general  shape  and  pro- 
portions this  element  is  so  similar  to  the  corresponding  elements  in 
figure  61,  h,  c,  that,  taken  together  with  the  similarity  of  the  other 
details  pointed  out  above,  it  seems  more  than  likely  that  all  three 
of  these  superfixes  are. one  and  the  same  element.  The  points  which 
have  led  the  writer  to  identify  glyphs  a,  &,  and  c  in  figure  61  as  forms 
for  the  great  cycle,  or  period  of  the  sixth  order,  may  be  summarized 
as  follows: 

1.  All  three  of  these  glyphs,  head-variant  as  well  as  normal  forms, 
are  made  up  of  the  corresponding  forms  of  the  cycle  sign  plus 
another  element,  a  superfix,  which  is  probably  the  determining  char- 
acteristic in  each  case. 

2.  All  three  of  these  superfixes  are  probably  identical,  thus  showing 
that  the  three  glyphs  in  which  they  occur  are  probably  variants  of 
the  same  sign. 

3.  All  three  of  these  glyphs  occur  in  numerical  series,  the  preceding 
term  of  which  in  each  case  is  a  cycle  sign,  thus  showing  that  by  posi- 
tion they  are  the  logical  ''next"  term  (the  sixth)  of  the  series. 

Let  us  next  examine  the  two  texts  in  which  great-great-cycle 
glyphs  may  occur.  (See  figs.  59,  60.)  The  two  glyphs  which  may 
possibly  be  identified  as  the  sign  for  this  period  are  shown  in  figure 
61,  d,  e. 

A  comparison  of  these  two  forms  shows  that  both  are  composed  of 
the  same  elements:  (1)  The  cycle  sign;  (2)  a  superfix  in  which  the 
hand  is  the  principal  element. 

The  superfix  in  figure  61,  cZ,  consists  of  a  hand  and  a  tassel-hke 
postfix,  not  unlike  the  upper  half  of  the  ending  signs  in  figure  37, 
l-q.  However,  in  the  present  case,  if  we  accept  the  hypothesis  that 
d  of  figure  61  is  the  sign  for  the  great-great  cycle,  we  are  obliged  to 
see  in  its  superfix  alone  the  essential  element  of  the  great-great-cycle 
sign,  since  the  rest  of  this  glyph  (the  lower  part)  is  quite  clearly  the 
normal  form  for  the  cycle. 

The  superfix  in  figure  61,  e,  consists  of  the  same  two  elements  as 
the  above,  with  the  shght  difference  that  the  hand  in  e  holds  a  rod. 
Indeed,  the  similarity  of  the  two  forms  is  so  close  that  in  default  of 


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BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


any  evidence  to  the  contrary  the  writer  believes  they  may  be  accepted 
as  signs  for  one  and  the  same  period,  namely,  the  great-great  cycle. 

The  points  on  which  this  conclusion  is  based  may  be  summarized 
as  follows: 

1.  Both  glyphs  are  made  up  of  the  same  elements — (a)  The  normal 
form  of  the  cycle  sign;  (b)  a  superfix  composed  of  a  hand  with  a  tassel- 
like postfix. 

2.  Both  glyphs  occur  in  numerical  series  the  next  term  but  one  of 
which  is  the  cycle,  showing  that  by  position  they  are  the  logical  next 
term  but  one,  the  seventh  or  great-great  cycle,  of  the  series. 

3.  Both  of  these  glyphs  stand  next  to  glyphs  which  have  been 
identified  as  great-cycle  signs,  that  is,  the  sixth  terms  of  the  series 
in  which  they  occur. 

By  this  same  line  of  reasoning  it  seems  probable  that  A2  in  figure  60 
is  the  sign  for  the  great-great-great  cycle,  although  this  fact  can  not 
be  definitely  estabhshed  because  of  the  lack  of  comparative  evidence. 

This  possible  sign  for  the  great-great-great  cycle,  or  period  of  the 
8th  order,  is  composed  of  two  parts,  just  hke  the  signs  for  the  great 
cycle  and  the  great-great  cycle  abeady  described.  These  are:  (1) 
The  cycle  sign;  (2)  a  superfix  composed  of  a  hand  and  a  semicircular 
postfix,  quite  distinct  from  the  superfixes  of  the  great  cycle  and 
great-great  cycle  signs. 

However,  since  there  is  no  other  inscription  known  which  presents 
a  number  composed  of  eight  terms,  we  must  lay  aside  this  line  of 
investigation  and  turn  to  another  for  further  light  on  this  point. 

An  examination  of  figure  60  shows  that  the  glyphs  which  we  have 
identified  as  the  signs  for  the  higher  periods  (A2,  A3,  A4,  and  A5,) 
contain  one  element  common  to  all — the  sign  for  the  cycle,  or  period 
of  144,000  days.  Indeed,  A5  is  composed  of  this  sign  alone  with 
its  usual  coefficient  of  9.  Moreover,  the  next  glyphs  (A6,  A7,  A8, 
and  A9  ^)  are  the  signs  for  the  katun,  tun,  uinal,  and  kin,  respectively, 
and,  together  with  A5,  form  a  regular  descending  series  of  5 
terms,  all  of  which  are  of  known  value. 

The  next  question  is.  How  is  this  glyph  in  the  sixth  place  formed  ? 
We  have  seen  that  in  the  only  three  texts  in  which  more  than  five 
periods  are  recorded  this  sign  for  the  sixth  period  is  composed  of  the 
same  elements  in  each:  (1)  The  cycle  sign;  (2)  a  superfix  containing 
two  ' 'shepherd's  crook"  infixes  and  surrounded  by  dots. 

Further,  we  have  seen  that  in  two  cases  in  the  inscriptions  the 
cycle  sign  has  a  coefficient  greater  than  13,  thus  showing  that  in  all 
probabiUty  20,  not  13,  cycles  made  1  great  cycle. 

Therefore,  since  the  great-cycle  signs  in  figure  61,  a-c,  are  composed 
of  the  cycle  sign  plus  a  superfix  (*),  this  superfix  must  have  the 
*    value  of  20  in  order  to  make  the  whole  glyph  have  the  value  of 


1  Glyph  A9  is  missing  but  undoubtedly  was  the  kiu  sign  and  coefficient. 


MORLBY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEEOGLYPHS  121 


20  cycles,  or  1  great  cycle  (that  is,  20  X  144,000  =  2,880,000) .  In  other 
words,  it  may  be  accepted  (1)  that  the  glyphs  in  figure  61,  a-c,  are 
signs  for  the  great  cycle,  or  period  of  the  sixth  place;  and  (2)  that 
the  great  cycle  was  composed  of  20  cycles  shown  graphically  by  two 
elements,  one  being  the  cycle  sign  itself  and  the  other  a  superfix 
having  the  value  of  20. 

It  has  been  shown  that  the  last  six  glyphs  in  figure  60  (A4,  A5,  A6, 
A7,  A8,  and  A9)  aU  belong  to  the  same  series.  Let  us  next  examine 
the  seventh  glyph  or  term  from  the  bottom  (A3)  and  see  how  it  is 
formed.  We  have  seen  that  in  the  only  two  texts  in  which  more  than 
six  periods  are  recorded  the  signs  for  the  seventh  period  (see  fig.  61, 
d,  e)  are  composed  of  the  same  elements  in  each:  (1)  The  cycle  sign; 
(2)  a  superfix  having  the  hand  as  its  principal  element.  We  have 
seen,  further,  that  in  the  only  three  places  in  which  great  cycles  are 
recorded  in  the  Maya  writing  (fig.  61,  a-c)  the  coefficient  in  every  case 
is  greater  than  13,  thus  showing  that  in  aU  probability  20,  not  13, 
great  cycles  made  1  great-great  cycle. 

Therefore,  since  the  great-great  cycle  signs  in  figure  %l,d,e,  are  com_ 
posed  of  the  cycle  sign  plus  a  superfix  (*),  this  superfix  must  [^g>^ 
have  the  value  of  400  (20  X  20)  in  order  to  make  the  whole  glyph  * 
have  the  value  of  20  great  cycles,  or  1  great-great  cycle  (20  X  2,880,000  = 
57,600,000).  In  other  words,  it  seems  highly  probable  (1)  that  the 
glyphs  in  figure  61,  d,  are  signs  for  the  great-great  cycle  or  period 
of  the  seventh  place,  and  (2)  that  the  great-great  cycle  was  composed 
of  20  great  cycles,  shown  graphically  by  two  elements,  one  being 
the  cycle  sign  itself  and  the  other  a  hand  having  the  value  of  400. 

It  has  been  shown  that  the  first  seven  glyphs  (A3,  A4,  A5,  A6,  A7, 
A8,  and  A9)  probably  aU  belong  to  the  same  series.  Let  us  next 
examine  the  eighth  term  (A2)  and  see  how  it  is  formed. 

As  stated  above,  comparative  evidence  can  help  us  no  further, 
since  the  text  under  discussion  is  the  only  one  which  presents  a  num- 
ber composed  of  more  than  seven  terms.  Nevertheless,  the  writer 
beUeves  it  will  be  possible  to  show  by  the  morphology  of  this,  the 
only  glyph  which  occupies  the  position  of  an  eighth  term,  that  it  is 
20  times  the  glyph  in  the  seventh  position,  and  consequently  that 
the  vigesimal  system  was  perfect  to  the  highest  known  unit  found 
in  the  Maya  writing. 

We  have  seen  (1)  that  the  sixth  term  was  composed  of  the  fifth  term 
plus  a  superfix  which  increased  the  fifth  20  times,  and  (2)  that  the 
seventh  term  was  composed  of  the  fifth  term  plus  a  superfix  which 
increased  the  fifth  400  times,  or  the  sixth  20  times. 

Now  let  us  examine  the  only  known  example  of  a  sign  for  the 
eighth  term  (A2,  fig.  60).  This  glyph  is  composed  of  (1)  the  cycle 
sign;  (2)  a  superfix  of  two  elements,  (a)  the  hand,  and  {h)  a  semi- 
circular element  in  which  dots  appear. 


122 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


But  this  same  hand  in  the  superfix  of  the  great-great  cycle  increased 
the  cycle  sign  400  times  (20x20;  see  A3,  fig.  60).  Therefore  we 
must  assume  the  same  condition  obtains  here.  And  finally,  since  the 
eighth  term  =20  X  20  X  20  X  cycle,  we  must  recognize  in  the  second 
element  of  the  superfix  (*)  a  sign  which  means  20. 

*  A  close  study  of  this  element  shows  that  it  has  two  impor- 
tant points  of  resemblance  to  the  superfix  of  the  great-cycle  glyph 
(see  A4,  fig.  60),  which  was  shown  to  have  the  value  20:  (1)  Both  ele- 
ments have  the  same  outline,  roughly  semicircular;  (2)  both  elements 
have  the  same  chain  of  dots  around  their  edges. 

Compare  this  element  in  A2,  figure  60,  with  the  superfixes  in  figure 
61,  a,  h,  bearing  in  mind  that  there  is  more  than  275  years'  differ- 
ence in  time  between  the  carving  of  A2,  figure  60,  and  a,  figure  61, 
and  more  than  200  years  between  the  former  and  figure  61,  h.  The 
writer  believes  both  are  variants  of  the  same  element,  and  conse- 
quently A2,  figure  60,  is  probably  composed  of  elements  which  signify 
20  X  400  (20  X  20)  X  the  cycle,  which  equals  one  great-great-great 
cycle,  or  term  of  the  eighth  place. 

Thus  on  the  basis  of  the  glyphs  themselves  it  seems  possible  to 
show  that  all  belong  to  one  and  the  same  numerical  series,  which 
progresses  according  to  the  terms  of  a  vigesimal  system  of  numera- 
tion. 

The  several  points  supporting  this  conclusion  may  be  summarized 
as  follows: 

1.  The  eight  periods  ^  in  figure  60  are  consecutive,  their  sequence 
being  uninterrupted  throughout.  Consequently  it  seems  probable 
that  all  belong  to  one  and  the  same  number. 

2.  It  has  been  shown  that  the  highest  three  period  glyphs  are  com- 
posed of  elements  which  multiply  the  cycle  sign  by  20,  400,  and 
8,000,  respectively,  which  has  to  be  the  case  if  they  are  the  sixth, 
seventh,  and  eighth  terms,  respectively,  of  the  Maya  vigesimal  system 
of  numeration. 

3.  The  highest  three  glyphs  have  numerical  coefficients,  just  like 
the  five  lower  ones;  this  tends  to  show  that  all  eight  are  terms  of 
the  same  numerical  series. 

4.  In  the  two  texts  which  alone  can  furnish  comparative  data  for 
this  sixth  term,  the  sixth-period  glyph  in  each  is  identical  with  A4, 
figure  60,  thus  showing  the  existence  of  a  sixth  period  in  the  inscrip- 
tions and  a  generally  ^  accepted  sign  for  it. 

5.  In  the  only  other  text  which  can  furnish  comparative  data  for 
the  seventh  term,  the  period  glyph  in  its  seventh  place  is  identical 

1  The  lowest  period,  the  kin,  is  missing.   See  A9,  fig.  60. 

2  The  use  of  the  word  "generally  "  seems  reasonable  here;  these  three  texts  come  from  widely  sepa- 
rated centers— Copan  in  the  extreme  southeast,  Palenque  in  the  extreme  west,  and  Tikal  in  the  central 
part  of  the  area. 


MORLET]      IN-TEODUCTION"  TO  STUDY  OF  MAYA  HIEEOGLYPHS  123 

with  A3,  figure  60;  thus  showing  the  existence  of  a  seventh  period  in 
the  inscriptions  and  a  generally  accepted  sign  for  it. 

6.  The  one  term  higher  than  the  cycle  in  the  Copan  text,  the  two 
terms  higher  in  the  Palenque  text,  and  the  three  terms  higher  in  this 
text,  are  all  built  on  the  same  basic  element,  the  cycle,  thus  showing 
that  in  each  case  the  higher  term  or  terms  is  a  continuation  of  the 
same  number,  not  a  Period-endmg  date,  as  suggested  by  Mr.  Good- 
man for  the  Copan  text. 

7.  The  other  two  texts,  showing  series  composed  of  more  than  five 
terms,  have  all  their  period  glyphs  in  an  unbroken  sequence  in  each, 
like  the  text  under  discussion,  thus  showing  that  in  each  of  these 
other  two  texts  all  the  terms  present  probably  belong  to  one  and 
the  same  number. 

8.  Finally,  the  two  occurrences  of  the  cycle  sign  with  a  coefiicient 
above  13,  and  the  three  occurrences  of  the  great-cycle  sign  with  a 
coefficient  above  13,  indicate  that  20,  not  13,  was  the  unit  of  progres- 
sion in  the  higher  numbers  in  the  inscriptions  just  as  it  was  in  the 
codices. 

Before  closing  the  discussion  of  this  unique  inscription,  there  is  one 
other  important  point  in  connection  with  it  which  must  be  considered, 
because  of  its  possible  bearing  on  the  meaning  of  the  Initial-series 
introducing  glyph. 

The  first  five  glyphs  on  the  east  side  of  Stela  10  at  Tikal  are  not 
illustrated  in  figure  60.  The  sixth  glyph  is  Al  in  figure  60,  and 
the  remaining  glyphs  in  this  figure  carry  the  text  to  the  bottom  of 
this  side  of  the  monument.  The  first  of  these  five  unfigured  glyphs 
is  very  clearly  an  Initial-series  introducing  glyph.  Of  this  there  can 
be  no  doubt.  The  second  resembles  the  day  8  Manik,  though  it  is 
somewhat  effaced.  The  remaining  three  are  unknown.  The  next 
glyph,  Al,  figure  60,  is  very  clearly  another  Initial-series  intro- 
ducing glyph,  having  all  of  the  five  elements  common  to  that  sign. 
Compare  Al  with  the  forms  for  the  Initial  series  introducing  glyph 
in  figure  24.  This  certainly  would  seem  to  indicate  that  an  Initial 
Series  is  to  follow.  Moreover,  the  fourth  glyph  of  the  eight-term 
number  following  in  A2-A9,  inclusive  (that  is,  A5),  records  Cycle  9," 
the  cycle  in  which  practically  all  Initial-series  dates  fall.  Indeed,  if 
A2,  A3,  and  A4  were  omitted  and  A5,  A6,  A7,  A8,  and  A9  were 
recorded  immediately  after  Al,  the  record  would  be  that  of  a  regular 
Initial-series  number  (9.  3.  6.  2.  0).  Can  this  be  a  matter  of  chance? 
If  not,  what  effect  can  A2,  A3,  and  A4  have  on  the  Initial-series 
date  in  Al,  A5-A9? 

The  writer  believes  that  the  only  possible  effect  they  could  have 
would  be  to  fix  Cycle  9  of  Maya  chronology  in  a  far  more  compre- 
hensive and  elaborate  chronological  conception,  a  conception  which 


124 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


indeed  staggers  the  imagination,  dealing  as  it  does  with  more  than 
five  million  years. 

If  these  eight  terms  all  belong  to  one  and  the  same  nmnerical 
series,  a  fact  the  writer  believes  he  has  established  in  the  foregoing 
pages,  it  means  that  Cycle  9,  the  first  historic  period  of  the  Maya 
civilization,  was  Cycle  9  of  Great  Cycle  19  of  Great-great  Cycle  11  of 
Great-great-great  Cycle  1.  In  other  words,  the  starting  point  of 
Maya  chronology,  which  we  have  seen  was  the  date  4  Ahau  8  Cumhu, 
9  cycles  before  the  close  of  a  Cycle  9,  was  in  reality  1.  11.  19.  0.  0.  0. 
0.  0.  4  Ahau  8  Cumliu,  or  simply  a  fixed  point  in  a  far  vaster  chrono- 
logical conception. 

Furthermore,  it  proves,  as  contended  by  the  writer  on  page  113, 
that  a  great  cycle  came  to  an  end  on  this  date,  4  Ahau  8  Cumliu. 
This  is  true  because  on  the  above  date  (1.  11.  19.  0.  0.  0.  0.  0.  4  Ahau 
8  Cumliu)  all  the  five  periods  lower  than  the  great  cycle  are  at  0.  It 
proves,  furthermore,  as  the  writer  also  contended,  that  the  date  4  Ahau 
8  Zotz,  13  cycles  in  advance  of  the  date  4  Ahau  8  Cumliu,  did  not  end 
a  great  cycle — 

1.  11.  19.   0.  0.  0.  0.  0.    4  Ahau  8  Cumhu 

13.  0.  0.  0.  0. 
1.  11.  18.   7.  0.  0.  0.  0.    4  Ahau  8  Zotz 

but,  on  the  contrary,  was  a  Cycle  7  of  Great  Cycle  18,  the  end  of 
which  (19.  0.  0.  0.  0.  0.  4  Ahau  8  Cumhu)  was  the  starting  point  of 
Maya  chronology. 

It  seems  to  the  writer  that  the  above  construction  is  the  only  one 
that  can  be  put  on  this  text  if  we  admit  that  the  eight  periods  in 
A2-A9,  figure  60,  all  belong  to  one  and  the  same  numerical  series. 

Furthermore,  it  would  show  that  the  great  cycle  in  which  fell  the 
first  historic  period  of  the  Maya  civilization  (Cycle  9)  was  itself  the 
closing  great  cycle  of  a  great-great  cycle,  namely.  Great-great  Cycle  1 1 : 

1.11.19.0.0.0.0.0. 

1.0.0.0.0.0. 
1.  12.   0.  0.  0.  0.  0.  0. 

That  is  to  say,  that  when  Great  Cycle  19  had  completed  itself,  Great- 
great  Cycle  12  would  be  ushered  in. 

We  have  seen  on  pages  108-1 13  that  the  names  of  the  cycles  followed 
one  another  in  this  sequence:  Cycle  1,  Cycle  2,  Cycle  3,  etc.,  to  Cycle 
13,  which  was  followed  by  Cycle  1,  and  the  sequence  repeated  itself. 
We  saw,  however,  that  these  names  probably  had  nothing  to  do  with 
the  positions  of  the  cycles  in  the  great  cycle;  that  on  the  contrary 
these  numbers  were  names  and  not  positions  in  a  higher  term. 

Now  we  have  seen  that  Maya  chronology  began  with  a  Cycle  1; 
that  is,  it  was  counted  from  the  end  of  a  Cycle  13.    Therefore,  the 


MORLBY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  125 


closing  cycle  of  Great  Cycle  19  of  Great-great  Cycle  11  of  Great-great- 
great  Cycle  1  was  a  Cycle  13,  that  is  to  say,  1.  11.  19.  0.  0.  0.  0.  0. 
4  Ahau  13  Cumhu  concluded  a  great  cycle,  the  closing  cycle  of  which 
was  named  Cycle  13.  This  large  number,  composed  of  one  great- 
great-great  cycle,  eleven  great-great  cycles,  and  nineteen  great  cycles, 
contains  exactly  12,780  cycles,  as  below: 

I  great-great-great  cycle  =  1  X  20  X  20  X  20  cycles  =  8,  000  cycles 

II  great-great  cycles  =  11  X  20  X  20  cycles  =  4,  400  cycles 
19  great  cycles  =  19  X  20  cycles  -      380  cycles 

12,  780  cycles 

But  the  closing  cycle  of  this  number  was  named  Cycle  13,  and  by 
deducting  all  the  multiples  of  13  possible  (983)  we  can  find  the  name 
of  the  first  cycle  of  Great-great-great  Cycle  1,  the  highest  Maya  time 
period  of  which  we  have  any  knowledge:  983x13  =  12,779.  And 
deducting  this  from  the  number  of  cycles  involved  (12,780),  we 
have — 

12,  780 
12,779 

1 

This  counted  backward  from  Cycle  1,  brings  us  again  to  a  Cycle  13  as 
the  name  of  the  first  cycle  in  the  Maya  conception  of  time.  In 
other  words,  the  Maya  conceived  time  to  have  commenced,  in  so  far 
as  we  can  judge  from  the  single  record  available,  with  a  Cycle  13, 
not  with  the  beginning  of  a  Cycle  1,  as  they  did  their  chronology. 

We  have  still  to  explain  Al,  figure  60.  This  glyph  is  quite  clearly 
a  form  of  the  Initial-series  introducing  glyph,  as  already  explained, 
in  which  the  five  components  of  that  glyph  are  present  in  usual  form: 
(1)  Trinal  superfix;  (2)  pair  of  comb-like  lateral  appendages ;  (3)  the 
tun  sign;  (4)  the  trinal  subfix;  (5)  the  variable  central  element,  here 
represented  by  a  grotesque  head. 

Of  these,  the  first  only  claims  our  attention  here.  The  trinal  super- 
fix  in  Al  (fig.  60) ,  as  its  name  signifies,  is  composed  of  three  parts, 
but,  unlike  other  forms  of  this  element,  the  middle  part  seems  to  be 
nothing  more  nor  less  than  a  numerical  dot  or  1 .  The  question  at 
once  arises,  can  the  two  flanking  parts  be  merely  ornamental  and 
the  whole  element  stand  for  the  number  1  ?  The  introducing  glyph 
at  the  beginning  of  this  text  (not  figured  here),  so  far  as  it  can  be 
made  out,  has  a  trinal  superfix  of  exactly  the  same  character — a  dot 
with  an  ornamental  scroll  on  each  side.  What  can  be  the  explanation 
of  this  element,  and  indeed  of  the  whole  glyph?  Is  it  one  great- 
great-great-great  cycle — a  period  twenty  times  as  great  as  the  one 
recorded  in  A2,  or  is  it  not  a  term  of  the  series  in  glyphs  A2-A9  ? 


126 


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[BULL.  57 


The  writer  believes  that  whatever  it  may  be,  it  is  at  least  not  a  mem- 
ber of  this  series,  and  in  support  of  his  belief  he  suggests  that  if  it 
were,  why  should  it  alone  be  retained  in  recording  all  Initial-series 
dates,  whereas  the  other  three — the  great-great-great  cycle,  the  great- 
great  cycle,  and  the  great-cycle  signs — have  disappeared. 

The  following  explanation,  the  writer  believes,  satisfactorily  accounts 
for  all  of  these  points,  though  it  is  advanced  here  only  by  way  of  sug- 
gestion as  a  possible  solution  of  the  meaning  of  the  Initial-series 
introducing  glyph.  It  is  suggested  that  in  Al  we  may  have  a  sign 
representing  ''eternity,"  'Hhis  world,"  ''time";  that  is  to  say,  a  sign 
denoting  the  duration  of  the  present  world-epoch,  the  epoch  of 
which  the  Maya  civilization  occupied  only  a  small  part.  The  middle 
dot  of  the  upper  element,  being  1,  denotes  that  this  world-epoch  is 
the  first,  or  present,  one,  and  the  whole  glyph  itself  might  mean  "the 
present  world."  The  appropriateness  of  such  a  glyph  ushering  in 
every  Initial-series  date  is  apparent.  It  signified  time  in  general, 
while  the  succeeding  7  glyphs  denoted  what  particular  day  of  time 
was  designated  in  the  inscription. 

But  why,  even  admitting  the  correctness  of  this  interpretation  of 
Al,  should  the  great-great-great  cycle,  the  great-great  cycle,  and 
the  great  cycle  of  their  chronological  scheme  be  omitted,  and 
Initial-series  dates  always  open  with  this  glyph,  which  signifies 
time  in  general,  followed  by  the  current  cycle  ?  The  answer  to  this 
question,  the  writer  believes,  is  that  the  cycle  was  the  greatest 
period  with  which  the  Maya  could  have  had  actual  experience.  It 
will  be  shown  in  Chapter  V  that  there  are  a  few  Cycle-8  dates 
actually  recorded,  as  well  as  a  half  a  dozen  Cycle-10  dates.  That 
is,  the  cycle,  which  changed  its  coefhcient  every  400  years,  was  a 
period  which  they  could  not  regard  as  never  changing  within  the 
range  of  human  experience.  On  the  other  hand,  it  was  the  shortest 
period  of  which  they  were  uncertain,  since  the  great  cycle  could 
change  its  coefhcient  only  every  8,000  years — practically  eternity  so 
far  as  the  Maya  were  concerned.  Therefore  it  could  be  omitted  as 
well  as  the  two  higher  periods  in  a  date  without  giving  rise  to  con- 
fusion as  to  which  great  cycle  was  the  current  one.  The  cycle,  on 
the  contrary,  had  to  be  given,  as  its  coefhcient  changed  every  400 
years,  and  the  Maya  are  known  to  have  recorded  dates  in  at  least 
three  cycles — Nos.  8,  9,  and  10.  Hence,  it  was  Great  Cycle  19  for 
8,000  years.  Great-great  Cycle  11  for  160,000,  and  Great-great-great 
Cycle  1  for  3,200,000  years,  whereas  it  was  Cycle  9  for  only  400  years. 
This,  not  the  fact  that  the  Maya  never  had  a  period  higher  than  the 
cycle,  the  writer  believes  was  the  reason  why  the  three  higher  periods 
were  omitted  from  Initial-series  dates — they  were  unnecessary  so  far 
as  accuracy  was  concerned,  since  there  could  never  be  any  doubt 
concerning  them. 


MOELEY]      II^TRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  127 


It  is  not  necessary  to  press  this  point  further,  though  it  is  beheved 
the  foregoing  conception  of  time  had  actually  been  worked  out  by 
the  Maya.  The  archaic  date  recorded  by  Stela  10  at  Tikal  (9.3.6.2.  0) 
makes  this  monument  one  of  the  very  oldest  in  the  Maya  territory; 
indeed,  there  is  only  one  other  stela  which  has  an  earlier  Initial  Series, 
Stela  3  at  Tikal.  In  the  archaic  period  from  which  tliis  monument 
dates  the  middle  dot  of  the  trinal  superfix  in  the  Initial-series  intro- 
ducing glyph  may  still  have  retained  its  numerical  value,  1,  but  in 
later  times  this  middle  dot  lost  its  numerical  characteristics  and 
frequently  appears  as  a  scroll  itself. 

The  early  date  of  Stela  10  makes  it  not  unlikely  that  this  process 
of  glyph  elaboration  may  not  have  set  in  at  the  time  it  was  erected, 
and  consequently  that  we  have  in  this  simplified  trinal  element  the 
genesis  of  the  later  elaborated  form;  and,  finally,  that  Al,  figure  60, 
may  have  meant  ^'the  present  world-epoch"  or  something  similar. 

In  concluding  the  presentation  of  these  three  numbers  the  writer 
may  express  the  opinion  that  a  careful  study  of  the  period  glyphs  in 
figures  58-60  will  lead  to  the  following  conclusions:  (1)  That  the  six 
periods  recorded  in  the  first,  the  seven  in  the  second,  and  the  eight  or 
nine  in  the  third,  all  belong  to  the  same  series  in  each  case;  and  (2) 
that  throughout  the  six  terms  of  the  first,  the  seven  of  the  second, 
and  the  eight  of  the  third,  the  series  in  each  case  conforms  strictly 
to  the  vigesimal  system  of  numeration  given  in  Table  VIII. 

As  mentioned  on  page  116  (footnote  2),  in  this  method  of  recording 
the  higher  numbers  the  kin  sign  may  sometimes  be  omitted  without 
affecting  the  numerical  value  of  the  series  wherein  the  omission 
occurs.  In  such  cases  the  coefficient  of  the  kin  sign  is  usually  pre- 
fixed to  the  uinal  sign,  the  coefficient  of  the  uinal  itself  standing 
above  the  uinal  sign.  In  figure  58,  for  example,  the  uinal  and  the 
kin  coefficients  are  both  0.  In  this  case,  however,  the  0  on  the  left 
of  the  uinal  sign  is  to  be  understood  as  belonging  to  the  kin  sign, 
which  is  omitted,  while  the  0  above  the  uinal  sign  is  the  uinal's  own 
coefficient  0.  Again  in  figure  59,  the  kin  sign  is  omitted  and  the  kin 
coefficient  1  is  prefixed  to  the  uinal  sign,  while  the  uinal's  own  coeffi- 
cient 12  stands  above  the  uinal  sign.  Similarly,  the  12  uinals  and 
17  kins  recorded  in  figure  56,  d,  might  as  well  have  been  written  as 
in  0  of  the  same  figure,  that  is,  with  the  kin  sign  omitted  and  its 
coefficient  17  prefixed  to  the  uinal  sign,  while  the  uinaFs  own  coeffi- 
cient 12  appears  above.  Or  again,  the  9  uinals  and  18  kins  recorded 
in  /  also  might  have  been  written  as  in  p,  that  is,  with  the  kin  sign 
omitted  and  the  kin  coefficient  18  prefixed  to  the  uinal  sign  while 
the  uinal's  own  coefiicient  9  appears  above. 

In  all  the  above  examples  the  coefficients  of  the  omitted  kin  signs 
are  on  the  left  of  the  uinal  signs,  while  the  uinal  coefficients  are  above 
the  uinal  signs.    Sometimes,  however,  these  positions  are  reversed. 


128 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


and  the  uinal  coefficient  stands  on  the  left  of  the  uinal  sign,  while  the 
kin  coefficient  stands  above.  This  interchange  in  certain  cases  prob- 
ably resulted  from  the  needs  of  glyphic  balance  and  symmetry. 
For  example,  in  figure  62,  a,  had  the  kin  coefficient  19  been  placed  on 
the  left  of  the  uinal  sign,  the  uinal  coefficient  4  would  have  been 
insufficient  to  fill  the  space  above  the  period  glyph,  and  consequently 
the  corner  of  the  glyph  block  would  have  appeared  ragged.  The 
use  of  the  19  above  and  the  4  to  the  left,  on  the  other  hand,  properly 
fills  this  space,  making  a  sjrmmetrical  glyph.  Such  cases,  however, 
are  unusual,  and  the  customary  position  of  the  kin  coefficient,  when 
the  kin  sign  is  omitted,  is  on  the  left  of  the  uinal  sign,  not  above 
it.    This  practice,  namely,  omitting  the  kin  sign  in  numerical  series, 


OOOO 


OOP 


Fig.  62.   Glyphs  showing  misplacement  of  the  kin  coeflacient  (a)  or  elimination  of  a  period  glyph  (6,  c): 
a,  Stela  E,  Quirigua;  h,  Altar  U,  Copan;  c,  Stela  J,  Copan. 

seems  to  have  prevailed  extensively  in  connection  with  both  Initial 
Series  and  Secondary  Series;  indeed,  in  the  latter  it  is  the  rule  to 
which  there  are  but  few  exceptions. 

The  omission  of  the  kin  sign,  while  by  far  the  most  common,  is  not 
the  only  example  of  glyph  omission  found  in  numerical  series  in  the 
inscriptions.  Sometimes,  though  very  rarely,  numbers  occur  in  which 
periods  other  than  the  kin  are  wanting.  A  case  in  point  is  figure  62,  &. 
Here  a  tun  sign  appears  with  the  coefficient  13  above  and  3  to  the  left. 
Since  there  are  only  two  coefficients  (13  and  3)  and  three  time  periods 
(tun,  uinal,  and  kin),  it  is  clear  that  the  signs  of  both  the  lower  periods 
have  been  omitted  as  well  as  the  coefficient  of  one  of  them.  In  c  of  the 
last-mentioned  figure  a  somewhat  different  practice  was  followed. 
Here,  although  three  time  periods  are  recorded — tuns,  uinals  and  kins — 
one  period  (the  uinal)  and  its  coefficient  have  been  omitted,  and  there 
is  nothing  between  the  0  kins  and  10  tuns.  Such  cases  are  exceed- 
ingly rare,  however,  and  may  be  disregarded  by  the  beginner. 

We  have  seen  that  the  order  of  the  periods  in  the  numbers  in  figure 
56  was  just  the  reverse  of  that  in  the  numbers  shown  in  figures  58 
and  59 ;  that  in  one  place  the  kins  stand  at  the  top  and  in  the  other 
at  the  bottom;  and  finally,  that  this  difference  was  not  a  vital  one, 
since  it  had  no  effect  on  the  values  of  the  numbers.  This  is  true, 
because  in  the  first  method  of  expressing  the  higher  numbers,  it 
matters  not  which  end  of  the  number  comes  first,  the  highest  or  the 


MORLBY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  129 

lowest  period,  so  long  as  its  several  periods  always  stand  in  the  same 
relation  to  each  other.  For  example,  in  figure  56,  g;,  6  cycles,  1 7  katuns, 
2  tuns,  10  uinals,  and  0  kins  represent  exactly  the  same  number  as 
0  kins,  10  uinals,  2  tuns,  17  katuns,  and  6  cycles;  that  is,  with  the 
lowest  term  first. 

It  was  explained  on  page  23  that  the  order  in  which  the  glyphs  are 
to  be  read  is  from  top  to  bottom  and  from  left  to  right.  Applying 
this  rule  to  the  inscriptions,  the  student  will  find  that  all  Initial  Series 
are  descending  series ;  that  in  reading  from  top  to  bottom  and  left 
to  right,  the  cycles  will  be  encountered  first,  the  katuns  next,  the 
tuns  next,  the  uinals,  and  the  kins  last.  Moreover,  it  wiU  be  found 
also  that  the  great  majority  of  Secondary  Series  are  ascending  series, 
that  is,  in  reading  from  top  to  bottom  and  left  to  right,  the  kins  will 
be  encountered  first,  the  uinals  next,  the  tuns  next,  the  katuns  next, 
and  the  cycles  last.  The  reason  why  Initial  Series  always  should  be 
presented  as  descending  series,  and  Secondary  Series  usually  as 
ascending  series  is  unknown;  though  as  stated  above,  the  order  in 
either  case  might  have  been  reversed  without  affecting  in  any  way 
the  numerical  value  of  either  series. 

This  concludes  the  discussion  of  the  first  method  of  expressing  the 
higher  numbers,  the  only  method  which  has  been  found  in  the 
inscriptions. 

Second  Method  of  Numeration 

The  other  method  by  means  of  which  the  Maya  expressed  their 
higher  numbers  (the  second  method  given  on  p.  103)  may  be  called 
'^numeration  by  position,"  since  in  this  method  the  numerical  value 
of  the  symbols  depended  solely  on  position,  just  as  in  our  own  deci- 
mal system,  in  which  the  value  of  a  figure  depends  on  its  distance 
from  the  decimal  point,  whole  numbers  being  written  to  the  left  and 
fractions  to  the  right.  The  ratio  of  increase,  as  the  word  decimal" 
implies,  is  10  throughout,  and  the  numerical  values  of  the  consecutive 
positions  increase  as  they  recede  from  the  decimal  point  in  each 
direction,  according  to  the  terms  of  a  geometrical  progression.  For 
example,  in  the  number  8888.0,  the  second  8  from  the  decimal  point, 
counting  from  right  to  left,  has  a  value  ton  times  greater  than  the  first 
8,  since  it  stands  for  8  tens  (80) ;  the  third  8  from  the  decimal  point 
similarly  has  a  value  ten  times  greater  than  the  second  8,  since  it 
stands  for  8  hundreds  (800) ;  finally,  the  fourth  8  has  a  value  ten 
times  greater  than  the  third  8,  since  it  stands  for  8  thousands 
(8,000).  Hence,  although  the  figures  used  are  the  same  in  each  case, 
each  has  a  different  numerical  value,  depending  solely  upon  its  posi- 
tion with  reference  to  the  decimal  point. 

In  the  second  method  of  writing  their  numbers  the  Maya  had 
devised  a  somewhat  similar  notation.  Their  ratio  of  increase  was  20  in 
all  positions  except  the  third.  The  value  of  these  positions  increased 
43508°— Bull.  57—15—9 


130 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


with  their  distance  from  the  bottom,  according  to  the  terms  of  the 
vigesimal  system  shown  in  Table  VIII.  This  second  method,  or 
'^numeration  by  position,"  as  it  may  be  called,  was  a  distinct  advance 
over  the  first,  since  it  required  for  its  expression  only  the  signs  for 
the  numerals  0  to  19,  inclusive,  and  did  not  involve  the  use  of  any 
period  glyphs,  as  did  the  first  method.  To  its  greater  brevity,  no 
doubt,  may  be  ascribed  its  use  in  the  codices,  where  numerical  calcu- 
lations running  into  numbers  of  5  and  6  terms  form  a  large  part  of 
the  subject  matter.  It  should  be  remembered  that  in  numeration 
by  position  only  the  normal  forms  of  the  numbers — bar  and  dot 
numerals — are  used.  This  probably  results  from  the  fact  that  head- 
variant  numerals  never  occur  independently,  but  are  always  prefixed 
to  some  other  glyph,  as  period,  day,  or  month  signs  (see  p.  104). 
Since  no  period  glyphs  are  used  in  numeration  by  position,  only 
normal-form  numerals,  that  is,  bar  and  dot  numerals,  can  appear. 

The  numbers  from  1  to  19,  inclusive,  are  expressed  in  this  method,  as 
shown  in  figure  39,  and  the  number  0  as  shown  in  figure  46.  As  aU 
of  these  numbers  are  below  20,  they  are  expressed  as  units  of  the  first 
place  or  order,  and  consequently  each  should  be  regarded  as  having 
been  multiplied  by  1 ,  the  numerical  value  of  the  first  or  lowest  position. 

The  number  20  was  expressed  in  two  difi"erent  ways:  (1)  By  the 
sign  shown  in  figure  45;  and  (2)  by  the  numeral  0  in  the  bottom 
place  and  the  numeral  1  in  the  next  place  above  it,  as  in  figure  63,  a. 
The  first  of  these  had  only  a  very  restricted  use  in  connection  with 
the  tonalamatl,  wherein  numeration  by  position  was  impossible,  and 
therefore  a  special  character  for  20  (see  fig.  45)  was  necessary. 
See  Chapter  VI. 

The  numbers  from  21  to  359,  inclusive,  involved  the  use  of  two 
places — the  kin  place  and  the  uinal  place — which,  according  to  Table 
VIII,  we  saw  had  numerical  values  of  1  and  20,  respectively.  For 
example,  the  number  37  was  expressed  as  shown  in  figure  63,  6.  The 
17  in  the  kin  place  has  a  value  of  17  (17  X  1)  and  the  1  in  the  uinal,  or 
second,  place  a  value  of  20  (1  (the  numeral)  X  20  (the  fixed  numerical 
value  of  the  second  place)).  The  sum  of  these  two  products  equals 
37.  Again,  300  was  written  as  in  figure  63,  c.  The  0  in  the  kin 
place  has  the  value  0  (0x1),  and  the  15  in  the  second  place  has  the 
value  of  300  (15  X  20),  and  the  sum  of  these  products  equals  300. 

To  express  the  numbers  360  to  7,199,  inclusive,  three  places  or 
terms  were  necessary — kins,  uinals,  and  tuns — of  which  the  last  had  a 
numerical  value  of  360.  (See  Table  VIII.)  For  example,  the  number 
360  is  shown  in  figure  63,  d.  The  0  in  the  lowest  place  indicates  that 
0  kins  are  involved,  the  0  in  the  second  place  indicates  that  0  uinals 
or  20 's  are  involved,  while  the  1  in  the  third  place  shows  that  there  is  1 
tun,  or  360,  kins  recorded  (1  (the  numeral)  X  360  (the  fixed  numerical 
value  of  the  third  position) ) ;  the  sum  of  these  three  products  equals 
360.    Agaui,  the  number  7,113  is  expressed  as  shown  in  figure  63,  e. 


MORLEY]      IITTKODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  131 

The  13  in  the  lowest  place  equals  13  (13x1);  the  13  in  the  second 
place,  260  (13x20);  and  the  19  in  the  third  place,  6,840  (19x360). 
The  sum  of  these  three  products  equals  7,113  (13  +  260  +  6,840). 


i  j  k 

Fig.  63.   Examples  of  the  second  metliod  of  numeration,  used  exclusively  in  the  codices. 

The  numbers  from  7,200  to  143,999,  inclusive,  involved  the  use  of 
four  places  or  terms — kins,  uinals,  tuns,  and  katuns — the  last  of 
which  (the  fourth  place)  had  a  numerical  value  of  7,200.  (See  Table 
VIII.)    For  example,  the  number  7,202  is  recorded  in  figure  63,/. 


132 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


The  2  in  the  first  place  equals  2  (2  X  1) ;  the  0  in  the  second  place,  0 
(0  X  20) ;  the  0  in  the  third  place,  0  (0  X  360) ;  and  the  1  in  the  fourth 
place,  7,200  (1  X  7,200).  The  sum  of  these  four  products  equals  7,202 
(2  +  0  +  0+  7,200).  Again,  the  number  100,932  is  recorded  in  figure 
63,  ^.  Here  the  12  in  the  first  place  equals  12  (12x1);  the  6  in  the 
second  place,  120  (6  X  20) ;  the  0  in  the  third  place,  0  (0  X  360) ;  and 
the  14  in  the  fourth  place,  100,800  (14x7,200).  The  sum  of  these 
four  products  equals  100,932  (12  +  120  +  0  +  100,800). 

The  numbers  from  144,000  to  2,879,999,  inclusive,  involved  the 
use  of  five  places  or  terms — kins,  uinals,  tuns,  katuns,  and  cycles. 
The  last  of  these  (the  fifth  place)  had  a  numerical  value  of  144,000. 
(See  Table  VIII.)  For  example,  the  number  169,200  is  recorded  in 
figure  63,  ti.  The  0  in  the  first  place  equals  0  (0x1);  the  0  in  the 
second  place,  0  (0x20);  the  10  in  the  third  place,  3,600  (10x360); 
the  3  in  the  fourth  place,  21,600  (3x7,200);  and  the  1  in  the  fifth  place, 
144,000  (1  X  144,000).  The  sum  of  these  five  products  equals  169,200 
(0  +  0  +  3,600  +  21,600  +  144,000).  Again,  the  number  2,577,301  is 
recorded  in  figure  63,  i.  The  1  in  the  first  place  equals  1  (1x1); 
the  3  in  the  second  place,  60  (3  X  20) ;  the  19  in  the  third  place,  6,840 
(19  X  360) ;  the  17  in  the  fourth  place,  122,400  (17  X  7,200) ;  and  the  17 
in  the  fifth  place,  2,448,000  (17x144,000).  The  sum  of  these  five 
products  equals  2,577,301  (1  +  60  +  6,480  +  122,400  +  2,448,000). 

The  writing  of  numbers  above  2,880,000  up  to  and  including 
12,489,781  (the  highest  number  found  in  the  codices)  involves  the 
use  of  six  places,  or  terms — kins,  uinals,  tuns,  katuns,  cycles,  and 
great  cycles — the  last  of  which  (the  sixth  place)  has  the  numerical 
value  2,880,000.  It  will  be  remembered  that  some  have  held  that 
the  sixth  place  in  the  inscriptions  contained  only  13  units  of  the  fifth 
place,  or  1,872,000  units  of  the  first  place.  In  the  codices,  however, 
there  are  numerous  calendric  checks  which  prove  conclusively  that 
in  so  far  as  the  codices  are  concerned  the  sixth  place  was  composed  of 
20  units  of  the  fifth  place.  For  example,  the  number  5,832,060  is 
expressed  as  in  figure  63,  j.  The  0  in  the  first  place  equals  0  (0x1); 
the  3  in  the  second  place,  60  (3  X  20) ;  the  0  in  the  third  place,  0  (0  X 
360) ;  the  3  0  in  the  fourth  place,  72,000  (10  X  7,200) ;  the  0  in  the  fifth 
place,  0  (0X144,000);  and  the  2  in  the  sixth  place,  5,760,000  (2x 
2,880,000).  The  sum  of  these  six  terms  equals  5,832,060  (0  +  60  +  0  + 
72,000  +  0+  5,760,000).  The  highest  number  in  the  codices,  as  ex- 
plained above,  is  12,489,781,  which  is  recorded  on  page  61  of  the 
Dresden  Codex.  This  number  is  expressed  as  in  figure  63,  Ic.  The  1 
in  the  first  place  equals  1  (1x1);  the  15  in  the  second  place,  300  (15  X 
20);  the  13  in  the  third  place,  4,680  (13x360);  the  14  in  the  fourth 
place,  100,800  (14x7,200);  the  6  in  the  fifth  place,  864,000  (6X 
144,000);  and  the  4  in  the  sixth  place,  11,520,000  (4X2,880,000). 
The  sum  of  these  six  products  equals  12,489,781  (1+300  +  4,680  + 
100,800  +  864,000  +  11,520,000). 


MORLBY]      INTRODUCTION  TO  STUDY  OP  MAYA  HIEROGLYPHS  133 

It  is  clear  that  in  numeration  by  position  the  order  of  the  units 
could  not  be  reversed  as  in  the  first  method  without  seriously  affecting 
their  numerical  values.  This  must  be  true,  since  in  the  second  method 
the  numerical  values  of  the  numerals  depend  entirely  on  their  position — 
that  is,  on  their  distance  above  the  bottom  or  first  term.  In  the  fij-st 
method,  the  multiphcands — the  period  glyphs,  each  of  which  had  a 
fixed  numerical  value — are  always  expressed  ^  with  their  correspond- 
ing multiphers — the  numerals  0  to  19,  inclusive;  in  other  words,  the 
period  glyphs  themselves  show  whether  the  series  is  an  ascending  or 
a  descending  one.  But  in  the  second  method  the  multiphcands  are 
not  expressed.  Consequently,  since  there  is  nothing  about  a  column 
of  bar  and  dot  numerals  which  in  itself  indicates  whether  the  series 
is  an  ascending  or  a  descending  one,  and  since  in  numeration  by 
position  a  fixed  starting  point  is  absolutely  essential,  in  their  sec- 
ond method  the  Maya  were  obliged  not  only  to  fijc  arbitrarily  the 
direction  of  reading,  as  from  bottom  to  top,  but  also  to  confine  them- 
selves exclusively  to  the  presentation  of  one  kind  of  series  only — that 
is,  ascending  series.  Only  by  means  of  these  two  arbitrary  rules  was 
confusion  obviated  in  numeration  by  position. 

However  dissimilar  these  two  methods  of  representing  the  numbers 
may  appear  at  first  sight,  fundamentally  they  are  the  same,  since 
both  have  as  their  basis  the  same  vigesimal  system  of  numeration. 
Indeed,  it  can  not  be  too  strongly  emphasized  that  throughout  the 
range  of  the  Maya  writings,  codices,  inscriptions,  or  Books  of  Chilam 
Balam  ^  the  several  methods  of  counting  time  and  recording  events 
found  in  each  are  all  derived  from  the  same  source,  and  all  are  expres- 
sions of  the  same  numerical  system. 

That  the  student  may  better  grasp  the  points  of  difference  between 
the  two  methods  they  are  here  contrasted : 

Table  XII.  COMPARISON  OF  THE  TWO  METHODS  OF  NUMERATION 


FIRST  METHOD 

1.  Use  confined  almost  exclusively  to  the 

inscriptions. 

2.  Numerals  represented  by  both  normal 

forms  and  head  variants. 

3.  Numbers  expressed  by  using  the  num- 

erals 0  to  19,  inclusive,  as  multipliers 
with  the  period  glyphs  as  multipli- 
cands. 

4.  Numbers  presented  as  ascending  or  de- 

scending series. 

5.  Direction  of  reading  either  from  bot- 

toin  to  top,  or  vice  versa, 

1  A  few  exceptions  to  this  have  been  noted  on  pp.  : 

2  The  Books  of  Chilan  Balam  have  been  included 
mind. 


SECOND  METHOD 

1.  Use  confined  exclusively  to  the  co- 
dices. 

2.  Numerals  represented  by  normal  forms 
exclusively. 

3.  Numbers  expressed  by  using  the  nu- 
merals 0  to  19,  inclusive,  as  multi- 
pliers in  certain  positions  the  fixed 
numerical  values  of  which  served  as 
multiplicands. 

4.  Numbers  presented  as  ascending  series 
exclusively. 

5 .  Direction  of  reading  from  bottom  to  top 
exclusively . 

127, 128. 

here  as  they  are  also  expressions  of  the  native  Maya 


134 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


We  have  seen  in  the  foregoing  pages  (I)  how  the  Maya  wr  ote  their  20 
numerals,  and  (2)  how  these  numerals  were  used  to  express  the  higher 
numbers.  The  next  question  which  concerns  us  is,  How  did  they  use 
these  numbers  in  their  calculations;  or  in  other  words,  how  was  their 
arithmetic  applied  to  their  calendar  ?  It  may  be  said  at  the  very 
outset  in  answer  to  this  question,  that  in  so  far  as  known,  numbers 
appear  to  Tuive  Tiad  hut  one  use  tJirougJiout  tlie  Maya  texts,  namely,  to 
express  the  time  elapsing  between  dates}  In  the  codices  and  the  inscrip- 
tions alike  all  the  numbers  whose  use  is  understood  have  been  found 
to  deal  exclusively  with  the  counting  of  time. 

This  highly  specialized  use  of  the  numbers  in  Maya  texts  has 
determined  the  first  step  to  be  taken  in  the  process  of  deciphering 
them.  Since  the  primary  unit  of  the  calendar  was  the  day,  all  numbers 
should  be  reduced  to  terms  of  this  unit,  or  in  other  words,  to  units  of 
the  first  order,  or  place. ^  Hence,  we  may  accept  the  following  as  the 
first  step  in  ascertaining  the  meaning  of  any  number: 

First  Step  in  Solving  Maya  Numbers 

Reduce  all  the  units  of  the  higher  orders  to  units  of  its  first,  or 
lowest,  order,  and  then  add  the  resulting  quantities  together. 

The  application  of  this  rule  to  any  Maya  number,  no  matter  of 
how  many  terms,  will  always  give  the  actual  number  of  primary  units 
which  it  contains,  and  in  this  form  it  can  be  more  conveniently  utiHzed 
in  connection  with  the  calendar  than  if  it  were  left  as  recorded,  that  is, 
in  terms  of  its  higher  orders. 

The  reduction  of  units  of  the  higher  orders  to  units  of  the  first  order 
has  been  explained  on  pages  105-133,  but  in  order  to  provide  the 
student  with  this  same  information  in  a  more  condensed  and  accessible 
form,  it  is  presented  in  the  following  tables,  of  which  Table  XIII  is 
to  be  used  for  reducing  numbers  to  their  primary  units  in  the  inscrip- 
tions, and  Table  XIV  for  the  same  purpose  in  the  codices. 

1  This  excludes,  of  course,  the  use  of  the  numerals  1  to  13,  inclusive,  in  the  day  names,  and  in  the  numer- 
ation of  the  cycles;  also  the  numerals  0  to  19,  inclusive,  when  used  to  denote  the  positions  of  the  days  in 
the  divisions  of  the  year,  and  the  position  of  any  period  in  the  division  next  higher. 

2  Various  methods  and  tables  have  been  devised  to  avoid  the  necessity  of  reducing  the  higher  terms  of 
Maya  numbers  to  units  of  the  first  order.  Of  the  former,  that  suggested  by  Mr.  Bowditch  (1910:  pp.  302- 
309)  is  probably  the  most  serviceable.  Of  the  tables  Mr.  Goodman's  Archseic  Annual  Calendar  and  Archaeic 
Chronological  Calendar  (1897)  are  by  far  the  best.  By  using  either  of  the  above  the  necessity  of  reducing  the 
higher  terms  to  units  of  the  first  order  is  obviated.  On  the  other  hand,  the  processes  by  means  of  which 
this  is  achieved  in  each  case  are  far  more  compUcated  and  less  easy  of  comprehension  than  those  of  the 
method  followed  in  this  book,  a  method  which  from  its  simpUcity  might  be  termed  perhaps  the  logical  way, 
since  it  reduces  all  quantities  to  a  primary  unit,  which  is  the  same  as  the  primary  unit  of  the  Maya  cal- 
endar. This  method  was  first  devised  by  Prof.  Ernst  Torstemann,  and  has  the  advantage  of  being  the  most 
readily  understood  by  the  beginner,  sufficient  reason  for  its  use  in  this- book. 


MORLEY]       INTKODUCTION  TO  STUDY  01?  MAYA  HIEROOLYPHS  135 


Table  XIII.  VALUES  OF  HIGHER 
PERIODS  IN  TERMS  OF  LOWEST, 
IN  INSCRIPTIONS 


1  great  cycle = 


cycle 
katim 

tun 
uinal 

kin 


2,880,000 
144,000 
7,200 
360 
20 
1 


Tablk  XIV.  VALUES  OF  HIGHER 
PERIODS  IN  TERMS  OF  LOWEST, 
IN  CODIGES 

1  unit  of  the  Gtli  place=2,880,000 
1  unit  of  the  5th  place  144,000 
1  unit  of  the  4th  place  7,200 
1  unit  of  the  3d  place  600 
1  unit  of  the  2d  place  20 
1  unit  of  the  1  st  place  1 


It  should  be  remembered,  in  using  these  tables,  that  each  of  the  signs 
for  the  periods  therein  given  has  its  own  particular  numerical  value, 
and  that  this  value  in  each  case  is  a  multiplicand  which  is  to  be  multi- 
plied by  the  numeral  attached  to  it  (not  shown  in  Table  XIII).  For 
example,  a  3  attached  to  the  katun  sign  reduces  to  21,600  units  of  the 
first  order  (3x7,200).  Again,  5  attached  to  the  uinal  sign  reduces 
to  100  units  of  the  first  order  (5  X  20) .  In  using  Table  XIV,  however, 
it  should  be  remembered  that  the  position  of  a  numeral  multiplier 
determines  at  the  same  time  that  multiplier's  multiplicand.  Thus  a 
5  in  the  third  place  indicates  that  the  5's  multiplicand  is  360,  the 
numerical  value  of  the  third  place,  and  such  a  term  reduces  to  1,800 
units  of  the  first  place  (5x360  =  1,800).  Again,  a  10  in  the  fourth 
place  indicates  that  the  lO's  multiplicand  is  7,200,  the  numerical  value 
corresponding  to  the  fourth  place,  and  such  a  term  reduces  to  72,000 
units  of  the  first  place. 

Having  reduced  all  the  terms  of  a  number  to  units  of  the  1st  order, 
the  next  step  in  finding  out  its  meaning  is  to  discover  the  date  from 
which  it  is  counted.    This  operation  gives  rise  to  the  second  step. 

Second  Step  in  Solving  Maya  Numbers 

Find  the  date  from  which  the  number  is  counted. 

This  is  not  always  an  easy  matter,  since  the  dates  from  which  Maya 
numbers  are  counted  are  frequently  not  expressed  in  the  texts ;  con- 
sequently, it  is  clear  that  no  single  rule  can  be  formulated  which  will 
cover  all  cases.  There  are,  however,  two  general  rules  which  will  be 
found  to  apply  to  the  great  majority  of  numbers  in  the  texts: 

Rule  1.  When  the  starting  point  or  date  is  expressed,  usually, 
though  not  invariably,  it  precedes  ^  the  number  counted  from  it. 

It  should  be  noted,  however,  in  connection  with  this  rule,  that  the 
starting  date  hardly  ever  immediately  precedes  the  number  from 
which  it  is  counted,  but  that  several  glyphs  nearly  always  stand 


1  This  number  is  formed  on  the  basis  of  20  cycles  to  a  great  cycle  (20X144,000=2,880,000).  The  writer 
assumes  that  he  has  established  the  fact  that  20  cycles  were  required  to  make  1  great  cycle,  in  the  inscrip- 
tions as  well  as  in  the  codices. 

2  This  is  true  in  spite  of  the  fact  that  in  the  codices  the  starting  points  frequently  appear  to  follow— that 
is,  they  stand  below— the  numbers  which  are  counted  from  them.  In  reality  such  cases  are  perfectly 
regular  and  conform  to  this  rule,  because  there  the  order  is  not  from  top  to  bottom  but  from  bottom  to  top, 
and,  therefore,  when  read  in  this  direction  the  dates  come  first. 


136 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


between.^  Certain  exceptions  to  the  above  rule  are  by  no  means 
rare,  and  the  student  must  be  continually  on  the  lookout  for  such 
reversals  of  the  regular  order.  These  exceptions  are  cases  in  which 
the  starting  date  (1)  follows  the  number  counted  from  it,  and  (2) 
stands  elsewhere  in  the  text,  entirely  disassociated  from,  and  unat- 
tached to,  the  number  counted  from  it. 

The  second  of  the  above-mentioned  general  rules,  covering  the 
majority  of  cases,  follows: 

Rule  2.  When  the  starting  point  or  date  is  not  expressed,  if  the 
number  is  an  Inital  Series  the  date  from  which  it  should  be  counted 
will  be  found  to  be  4  Ahau  8  Cumliu.^ 

This  rule  is  particularly  useful  in  deciphering  numbers  in  the 
inscriptions.  For  example,  when  the  student  finds  a  number  which 
he  can  identify  as  an  Initial  Series,^  he  may  assume  at  once  that  such 
a  number  in  all  probability  is  counted  from  the  date  4  Ahau  8  Cumhu, 
and  proceed  on  this  assumption.  The  exceptions  to  this  rule,  that 
is,  cases  in  which  the  starting  point  is  not  expressed  and  the  number 
is  not  an  Initial  Series,  are  not  numerous.  No  rule  can  be  given  cov- 
ering all  such  cases,  and  the  starting  points  of  such  numbers  can  be 
determined  only  by  means  of  the  calculations  given  under  the  third 
and  fourth  steps,  below. 

Having  determined  the  starting  point  or  date  from  which  a  given 
number  is  to  be  counted  (if  this  is  possible),  the  next  step  is  to  find 
out  which  way  the  count  runs;  that  is,  whether  it  is  forward  from 
the  starting  point  to  some  later  date,  or  whether  it  is  hackward  from 
the  starting  point  to  some  earlier  date.  This  process  may  be  called 
the  tliird  step. 

Third  Step  in  Solving  Maya  Numbers 

Ascertain  whether  the  number  is  to  be  counted  forward  or  backward 
from  its  starting  point. 

It  may  be  said  at  the  very  outset  in  this  connection  that  the  over- 
whelming majority  of  Maya  numbers  are  coVinted  forward  from  their 
starting  points  and  not  backward.  In  other  words,  they  proceed  from 
earlier  to  later  dates  and  not  vice  versa.  Indeed,  the  preponderance 
of  the  former  is  so  great,  and  the  exceptions  are  so  rare,  that  the 
student  should  always  proceed  on  the  postulate  that  the  count  is 
forward  until  proved  definitely  to  be  otherwise. 

1  These  intervening  glyphs  the  writer  believes,  as  stated  in  Chapter  II,  are  those  which  tell  the  real  story 
of  the  inscriptions. 

2  Only  two  exceptions  to  this  rule  have  been  noted  throughout  the  Maya  territory:  (1)  The  Initial  Series 
on  the  east  side  of  Stela  C  at  Quirigua,  and  (2)  the  tablet  from  the  Temple  of  the  Cross  at  Palenque.  It 
has  been  explained  that  both  of  these  Initial  Series  are  counted  from  the  date  4  Ahau  8  Zotz. 

3  In  the  inscriptions  an  Initial  Series  may  always  be  identified  by  the  so-called  introducing  glyph  (see 
fig.  24)  which  invariably  precedes  it. 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


137 


In  the  codices,  moreover,  when  the  count  is  backward,  or  contrary 
to  the  general  practice,  the  fact  is  clearly  indicated  ^  by  a  special  char- 
acter. This  character,  although  attached  only  to  the  lowest  term  ^ 
of  the  number  which  is  to  be  counted  backward,  is  to  be  interpreted 
as  applying  to  all  the  other  terms  as  well,  its  effect  extending  to  the 
number  as  a  whole.  This  "backward  sign"  (shown  in  fig.  64)  is  a 
circle  drawn  in  red  around  the  lowest  term  of  the  number  which  it 
affects,  and  is  surmounted  by  a  knot  of  the  same  color.  An  example 
covering  the  use  of  this  sign  is  given  in  figure  64.  Although  the 
"backward  sign"  in  this  figure  surrounds  only  the  _ 
numeral  in  the  first  place,  0,  it  is  to  be  interpreted,  as 
we  have  seen,  as  applying  to  the  2  in  the  second  place 
and  the  6  in  the  third  place.  This  number,  expressed 
as  6  tuns,  2  uinals,  and  0  kins,  reduces  to  2,200  units 
of  the  first  place,  and  in  this  form  may  be  more  readily 
handled  (first  step).  Since  the  starting  point  usually 
precedes  the  number  counted  from  it  and  since  iii  figure 
64  the  number  is  expressed  by  the  second  method,  its 
starting  point  will  be  found  standing  below  it.  This  ^^^^^^ 
follows  from  the  fact  that  in  numeration  by  position  showing  the 
the  order  is  from  bottom  to  top.    Therefore  the  start-  ""'^^j^^l""^- 

^  nus   or  back- 

ing point  from  which  the  2,200  recorded  in  figure  64  is    ward"  sign  in 

counted  will  be  found  to  be  below  it,  that  is,  the  date  ^^^^o^^^®^- 

4  Ahau  8  Cumhu^  (second  step).    Finally,  the  red  circle  and  knot 

surrounding  the  lowest  (0)  term  of  this  2,200  indicates  that  this 

number  is  to  be  counted  hackward  from  its  starting  point,  not 

forward  (t'hird  step). 

On  the  other  hand,  in  the  inscriptions  no  special  character  seems 
to  have  been  used  with  a  number  to  indicate  that  it  was  to  be  counted 
backward;  at  least  no  such  sign  has  yet  been  discovered.  In  the 
inscriptions,  therefore,  with  the  single  exception  ^  mentioned  below, 
the  student  can  only  apply  the  general  rule  given  on  page  136,  that 
in  the  great  majority  of  cases  the  count  is  forward.  This  rule  will  be 
found  to  apply  to  at  least  nine  out  of  every  ten  numbers.  The  excep- 
tion above  noted,  that  is,  where  the  practice  is  so  uniform  as  to  render 
possible  the  formulation  of  an  unfailing  rule,  has  to  do  with  Initial 
Series.  This  rule,  to  which  there  are  no  known  exceptions,  may  be 
stated  as  foUows: 

Rule  1.  In  Initial  Series  the  count  is  always  forward,  and,  in  general 
throughout  the  inscriptions.  The  very  few  cases  in  which  the  count 
is  backward,  are  confined  chiefly  to  Secondary  Series,  and  it  is  in 

1  Professor  Forstemann  has  pointed  out  a  few  cases  in  the  Dresden  Codex  in  which,  although  the  count 
is  backward,  the  special  character  indicating  the  fact  is  wanting  (fig.  64),   (See  Bulletin  28,  p.  401.) 

2  There  are  a  few  cases  in  which  the  "backward  sign"  includes  also  the  numeral  in  the  second  position. 

3  In  the  text  wherein  this  number  is  found  the  date  4  Ahau  8  Cumhu  stands  below  the  loM^est  term. 

1 1t  should  be  noted  here  that  in  the  u  kahlay  katunob  also,  from  the  Books  of  Chilan  Balam,  the  count  is 
always  forward. 


138 


BUREAU  OF  AMERICAN  ETHIs^OLOGY 


[BULL.  57 


dealing  with  this  kind  of  series  that  the  student  will  find  the  greatest 
number  of  exceptions  to  the  general  rule. 

Having  determined  the  direction  of  the  count,  whether  it  is  forward 
or  backward,  the  next  (fourtli)  step  may  be  given. 

Fourth  Step  in  Solving  Maya  Numbers 

To  count  the  number  from  its  starting  point. 

We  have  come  now  to  a  step  that  involves  the  consideration  of 
actual  arithmetical  processes,  which  it  is  thought  can  be  set  forth 
much  more  clearly  by  the  use  of  specific  examples  than  by  the  state- 
ment of  general  rules.  Hence,  we  will  formulate  our  rules  after  the 
processes  which  they  govern  have  been  fully  explained. 

In  counting  any  number,  as  31,741,  or  4.8.3.1  as  it  would  be 
expressed  in  Maya  notation,^  from  any  date,  as  4  Ahau  8  Cumhu, 
there  are  four  unknown  elements  which  have  to  be  determined  before 
we  can  write  the  date  which  the  count  reaches.    These  are: 

1.  The  day  coefficient,  which  must  be  one  of  the  numerals  1  to  13, 
inclusive. 

2.  The  day  name,  which  must  be  one  of  the  twenty  given  in  Table  I. 

3.  The  position  of  the  day  in  some  division  of  the  year,  which  must 
be  one  of  the  numerals  0  to  10,  inclusive. 

4.  The  name  of  the  division  of  the  year,  which  must  be  one  of  the 
nineteen  given  in  Table  III. 

These  four  imknown  elements  all  have  to  be  determined  from  (1 ) 
the  starting  date,  and  (2)  the  number  w^hlch  is  to  be  counted  from  it. 

If  the  student  will  constantly  bear  in  mind  that  all  Maya  sequences, 
whether  the  day  coefficients,  day  signs,  positions  in  the  divisions  of 
the  year,  or  what  not,  are  absolutely  continuous,  repeating  themselves 
without  any  break  or  interruption  whatsoever,  he  will  better  under- 
stand the  calculations  which  follow. 

It  was  explained  in  the  text  (see  pp.  41-44)  and  also  shown  graph- 
ically in  the  tonalamatl  wheel  (pi.  5)  that  after  the  day  coefficients 
had  reached  the  number  13  they  returned  to  1,  following  each  other 
indefinite^  in  this  order  without  interruption.  It  is  clear,  therefore, 
that  the  highest  multiple  of  13  which  the  given  number  contains  may 
be  subtracted  from  it  without  affecting  in  any  way  the  value  of  the 
day  coefficient  of  the  date  which  the  number  will  reach  when  counted 
from  the  starting  point.  This  is  true,  because  no  matter  what  the 
day  coefficient  of  the  starting  point  may  be,  any  multiple  of  13  will 
always  bring  the  count  back  to  the  same  day  coefficient. 

1  For  transcribing  the  Maya  numerical  notation  into  the  characters  of  our  own  Arabic  notation  Maya 
students  have  adopted  the  practice  of  writing  the  various  terms  from  left  to  right  in  a  descending  series, 
as  the  units  of  our  decimal  system  are  written.  For  example,  4  katuns,  8  tuns,  3  uinals,  and  1  kin  are 
written  4.8.3.1;  and  9  cycles,  16  katuns,  1  tun,  0  uinal,  and  0  kins  are  written  9.16.1.0.0.  According  to  this 
method,  the  highest  term  in  each  number  is  written  on  the  left,  the  next  lower  on  its  right,  the  next  lower 
on  the  right  of  that,  and  so  on  down  through  the  units  of  the  first,  or  lowest,  order.  This  notation  is  very 
convenient  for  transcribing  the  Maya  numbers  and  will  be  followed  hereafter. 


MORLEY]      INTEODUCTION  TO  STUDY  OF  MAYA  HIEKOGLYPHS  139 

Taking  up  the  number,  31,741,  which  wo  have  chosen  for  our  first 
example,  let  us  deduct  from  it  the  highest  multiple  of  13  which  it 
contains.  This  will  be  found  by  dividing  the  number  by  13,  and 
multiplying  the  wJiole-number  fart  of  the  resulting  quotient  by  13: 
31,741 -13  =  2,441t§3.  Multiplymg  2,441  by  13,  we- have  31,733, 
which  is  the  highest  multiple  of  13  that  31,741  contains  ;  consequently 
it  may  be  deducted  from  31,741  without  affecting  the  value  of  the 
resulting  day  coefficient:  31,741  -31,733  =8.  In  the  example  under 
consideration,  therefore,  8  is  the  number  which,  if  counted  from  the 
day  coefficient  of  the  starting  point,  will  give  the  day  coefficient  of 
the  resulting  date.  In  other  words,  after  dividing  by  13  the  only 
part  of  the  resulting  quotient  which  is  used  in  determining  the  new 
day  coefficient  is  the  numerator  of  the  fractional  part.^  Hence  the 
following  rule  for  determining  the  first  unknown  on  page  138  (the  day 
coefficient) : 

Rule  1.  To  find  the  new  day  coefficient  divide  the  given  number 
by  13,  and  count  forward  the  numerator  of  the  fractional  Dart  of  the 
resulting  quotient  from  the  starting  point  if  the  count  is  forward, 
and  backward  if  the  count  is  backward,  deducting  13  in  either  case 
from  the  resulting  number  if  it  should  exceed  13. 

Applying  this  rule  to  31,741,  we  have  seen  above  that  its  division 
by  13  gives  as  the  fractional  part  of  the  quotient  Assuming  that 
the  count  is  forward  from  the  starting  point,  4  Aliau  8  Cumliu,  if  8 
(the  numerator  of  the  fractional  part  of  the  quotient)  be  counted 
forward  from  4,  the  day  coefficient  of  the  starting  point  (4  Ahau 
8  Cumhu),  the  day  coefficient  of  the  resulting  date  will  be  12  (4  +  8). 
Since  this  number  is  below  13,  the  last  sentence  of  the  above  rule  has 
no  application  in  this  case.  In  counting  forward  31,741  from  the 
date  4  Ahau  8  Cumliu,  therefore,  the  day  coefficient  of  the  resulting 
date  will  be  12;  thus  we  have  determined  our  first  unknown.  Let 
us  next  find  the  second  unknown,  the  day  sign  to  which  this  12  is 
prefixed. 

It  was  explained  on  page  37  that  the  twenty  day  signs  given  in 
Table  I  succeed  one  another  in  endless  rotation,  the  first  following 
immediately  the  twentieth  no  matter  which  one  of  the  twenty  was 
chosen  as  the  first.  Consequently,  it  is  clear  that  the  highest  mul- 
tiple of  20  which  the  given  number  contains  may  be  deducted  from  it 
without  affecting  in  any  way  the  name  of  the  day  sign  of  the  date 
which  the  number  will  reach  when  counted  from  the  starting  point. 
This  is  true  because,  no  matter  what  the  day  sign  of  the  starting 
point  may  be,  any  multiple  of  20  will  always  bring  the  count  back  to 
the  same  day  sign. 

1  The  reason  for  rejecting  all  parts  of  the  quotient  except  the  numerator  of  the  fractional  part  is  that  this 
part  alone  shows  the  actual  number  of  units  which  have  to  be  counted  either  forward  or  backward,  as  the 
count  may  be,  in  order  to  reach  the  number  which  exactly  uses  up  or  finishes  the  dividend— the  last  unit 
of  the  number  which  has  to  be  counted. 


140 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


Returning  to  the  number  31,741,  let  us  deduct  from  it  the  highest 
multiple  of  20  which  it  contains,  found  by  dividing  the  number  by 
20  and  multiplying  the  whole  number  part  of  the  resulting  quotient 
by  20;  31,741 -^ 20  =  1,587^.  Multiplying  1,587  by  20,  we  have 
31,740,  which  is  the  highest  multiple  of  20  that  31,741  contains,  and 
which  maybe  deducted  from  31,741  without  affecting  the  resulting 
day  sign;  31,741—31,740  =  1.  Therefore  in  the  present  example  1 
is  the  number  which,  if  counted  forward  from  the  day  sign  of  the 
starting  point  in  the  sequence  of  the  20  day  signs  given  in  Table  I, 
will  reach  the  day  sign  of  the  resulting  date.  In  other  words,  after 
dividing  by  20  the  only  part  of  the  resulting  quotient  which  is  used 
in  determining  the  new  day  sign  is  the  numerator  of  the  fractional 
part.  Thus  we  may  formulate  the  rule  for  determining  the  second 
unknown  on  page  138  (the  day  sign): 

Rule  2.  To  find  the  new  day  sign,  divide  the  given  number  by  20, 
and  count  forward  the  numerator  of  the  fractional  part  of  the  result- 
ing quotient  from  the  starting  point  in  the  sequence  of  the  twenty 
day  signs  given  in  Table  I,  if  the  count  is  forward,  and  backward  if 
the  count  is  backward,  and  the  sign  reached  will  be  the  new  day  sign. 

Applying  this  rule  to  31,741,  we  have  seen  above  that  its  division 
by  20  gives  us  as  the  fractional  part  of  the  quotient,  Since  the 
count  was  forward  from  the  starting  point,  if  1  (the  numerator  of  the 
fractional  part  of  the  quotient)  be  counted  forward  in  the  sequence 
of  the  20  day  signs  in  Table  I  from  the  day  sign  of  the  starting  point, 
Ahau  (4  Ahau  8  Cumhu),  the  day  sign  reached  will  be  the  day  sign 
of  the  resulting  date.  Counting  forward  1  from  Ahau  in  Table  I, 
the  day  sign  Imix  is  reached,  and  Imix,  therefore,  will  be  the  new 
day  sign.    Thus  our  second  unknown  is  determined. 

By  combining  the  above  two  values,  the  12  for  the  first  unknown 
and  Imix  for  the  second,  we  can  now  say  that  in  counting  forward 
31,741  from  the  date  4  Ahau  8  Cumhu,  the  day  reached  will  be  12  Imix. 
It  remains  to  find  what  position  this  particular  day  occupied  in  the 
365-day  year,  or  haab,  and  thus  to  determine  the  third  and  fourth 
unknowns  on  page  138.  Both  of  these  may  be  found  at  one  time  by 
the  same  operation. 

It  was  explained  on  pages  44-51  that  the  Maya  year,  at  least  in 
so  far  as  the  calendar  was  concerned,  contained  only  365  days,  divided 
into  18  uinals  of  20  days  each,  and  the  xma  Icaha  Tcin  of  5  days;  and 
further,  that  when  the  last  position  in  the  last  division  of  the  year 
(4  XJayeb)  was  reached,  it  was  followed  without  interruption  by  the 
first  position  of  the  first  division  of  the  next  year  (0  Pop);  and, 
finally,  that  this  sequence  was  continued  indefinitely.  Consequently 
it  is  clear  that  the  highest  multiple  of  365  which  the  given  number 
contains  may  be  subtracted  from  it  without  affecting  in  any  way  the 
position  in  the  year  of  the  day  which  the  number  will  reach  when 


MORLBY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  141 


counted  from  the  starting  point.  This  is  true,  because  no  matter 
what  position  in  the  year  the  day  of  the  starting  point  may  occupy, 
any  multiple  of  365  will  bring  the  count  back  again  to  the  same 
position  in  the  year. 

Returning  again  to  the  number  31,741,  let  us  deduct  from  it  the 
highest  multiple  of  365  which  it  contains.  This  will  be  found  by 
dividing  the  number  by  365  and  multiplying  the  whole  number  part 
of  the  resulting  quotient  by  365:  31,741  X  365  =  86f|i.  Multiplying 
86  by  365,  we  have  31,390,  which  is  the  highest  multiple  that  31,741 
contains.  Hence  it  may  be  deducted  from  31,741  without  affecting 
the  position  in  the  year  of  the  resulting  day;  31,741—31,390  =  351. 
Therefore,  in  the  present  example,  351  is  the  number  which,  if 
counted  forward  from  the  year  position  of  the  starting  date  in  the 
sequence  of  the  365  positions  in  the  year,  given  in  Table  XV,  will 
reach  the  position  in  the  year  oi  the  day  of  the  resulting  date.  This 
enables  us  to  formulate  the  rule  for  determining  the  third  and  fourth 
unknowns  on  page  138  (the  position  in  the  year  of  the  dav  of  the  re- 
sulting date) : 

Rule  3.  To  find  the  position  in  the  year  of  the  new  day,  divide 
the  given  number  by  365  and  count  forward  the  numerator  of  the 
fractional  part  of  the  resulting  quotient  from  the  year  position  of 
the  starting  point  in  the  sequence  of  the  365  positions  of  the  year 
shown  in  Table  XV,  if  the  count  is  forward;  and  backward  if  the 
count  is  backward,  and  the  position  reached  will  be  the  position  in 
the  year  which  the  day  of  the  resulting  date  will  occupy. 

Table  XV.  THE  365  POSITIONS  IN  THE  MAYA  YEAR 


Pop 

o 

P 

Zip 

Zotz 

Tzec 

Xul 

Yaxkin 

Mol 

Chen 

Yax 

Zac 

O 

Mac 

B 

t 

M 

Muan 

Pax 

Kayab 

Cumhu 

Uayeb 

Position  

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

( 

Do  

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

Do  

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

Do  

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

Do  

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

Do  

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

Do  

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

Do  

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

Do  

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

Do  

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

Do  

10 

10 

10 

10 

10 

10 

10 

10 

10 

10 

10 

10 

10 

10 

10 

10 

10 

10 

Do  

11 

11 

11 

11 

11 

11 

11 

11 

11 

11 

11 

11 

11 

11 

11 

11 

11 

11 

Do  

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

Do  -  

13 

13 

13 

13 

13 

13 

13 

13 

13 

13 

13 

13 

13 

13 

13 

13 

13 

13 

Do  

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

Do  

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

Do  

16 

16 

16 

16 

16 

16 

16 

16 

16 

16 

16 

16 

16 

16 

16 

16 

16 

16 

Do  

17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

Do  

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

Do  

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

142 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


Applying  this  rule  to  the  number  31,741,  we  have  seen  above  that 
its  division  by  365  gives  351  as  the  numerator  of  the  fractional  part  of 
its  quotient.  Assuming  that  the  count  is  forward  from  the  starting 
point,  it  will  be  necessary,  therefore,  to  count  351  forward  in  Table 
XV  from  the  position  8  Cumhu,  the  position  of  the  day  of  the  starting 
point,  4  Ahau  8  Cumhu. 

A  glance  at  the  month  of  Cumhu  in  Table  XV  shows  that  after  the 
position  8  Cumhu  there  are  11  positions  in  that  month;  adding  to 
these  the  5  in  Uayeb,  the  last  division  of  the  year,  there  will  be  in  all 
16  more  positions  before  the  first  of  the  next  year.  Subtracting 
these  from  351,  the  total  number  to  be  counted  forward,  there  remains 
the  number  335  (351-16),  which  must  be  counted  forward  in  Table 
XV  from  the  beginning  of  the  year.  Since  each  of  the  months  has 
20  positions,  it  is  clear  that  16  months  will  be  used  before  the  month 
is  reached  in  which  will  fall  the  335th  position  from  the  beginning  of 
the  year.  In  other  words,  320  positions  of  our  335  will  exactly  use 
up  all  the  positions  of  the  first  16  months,  namely,  Pop,  Uo,  Zip, 
Zotz,  Tzec,  Xul,  Yaxkin,  Mol,  Chen,  Yax,  Zac,  Ceh,  Mac,  Kankin, 
Muan,  Pax,  and  will  bring  us  to  the  beginning  of  the  17th  month 
(Kayab)  with  still  15  more  positions  to  count  forward.  If  the  student 
will  refer  to  this  month  in  Table  XV  he  will  see  that  15  positions 
counted  forward  in  this  month  will  reach  the  position  14  Kayab, 
which  is  also  the  position  reached  by  counting  forward  31,741  posi- 
tions from  the  starting  position  8  Cumhu. 

Having  determined  values  for  all  of  the  unknowns  on  page  138,  we 
can  now  say  that  if  the  number  31,741  be  counted  forward  from  the 
date  4  Ahau  8  Cumhu,  the  date  12  Imix  14  Kayab  will  be  reached. 
To  this  latter  date,  i.  e.,  the  date  reached  by  any  count,  the  name  ''ter- 
minal date"  has  been  given.  The  rules  indicating  the  processes  by 
means  of  which  this  terminal  date  is  reached  apply  also  to  examples 
where  the  count  is  backward,  not  forward,  from  the  starting  point. 
In  such  cases,  as  the  rules  say,  the  only  difference  is  that  the 
numerators  of  the  fractional  parts  of  the  quotients  resulting  from  the 
different  divisions  are  to  be  counted  backward  from  the  starting 
points,  instead  of  forward  as  in  the  example  above  given. 

Before  proceeding  to  apply  the  rules  by  means  of  which  our  fourth 
step  or  process  (see  p.  138)  may  be  carried  out,  a  modification  may 
sometimes  be  introduced  which  will  considerably  decrease  the  size 
of  the  number  to  be  counted  without  affecting  the  values  of  the 
several  parts  of  its  resulting  terminal  date.  * 

We  have  seen  on  pages  51-60  that  in  Maya  chronology  there  were 
possible  only  18,980  different  dates — that  is,  combinations  of  the  260 
days  and  the  365  positions  of  the  year — and  further,  that  any  given 
day  of  the  260  could  return  to  any  given  position  of  the  365  only  after 
the  lapse  of  18,980  days^  or  52  years. 


MORLBY]       IITTKODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  143 

Since  the  foregoing  is  true,  it  follows,  that  this  number  18,980  or 
any  multiple  thereof,  may  be  deducted  from  the  number  which  is  to 
be  counted  without  affecting  in  any  way  the  terminal  date  which  the 
number  will  reach  when  counted  from  the  starting  point.  It  is 
obvious  that  this  modification  applies  only  to  numbers  which  are 
above  18,980,  all  others  being  divided  by  13,  20,  and  365  directly,  as 
indicated  in  rules  1,  2,  and  3,  respectively.  This  enables  us  to 
formulate  another  rule,  which  should  be  applied  to  the  number  to 
be  counted  before  proceeding  with  rules  1,  2,  and  3  above,  if  that 
number  is  above  18,980. 

Rule.  If  the  number  to  be  counted  is  above  18,980,  first  deduct 
from  it  the  highest  multiple  of  18,980  which  it  contains. 

This  rule  should  be  applied  whenever  possible,  since  it  reduces  the 
size  of  the  number  to  be  handled,  and  consequently  involves  fewer 
calculations. 

In  Table  XVI  are  given  80  Calendar  Rounds,  that  is,  80  multiples 
of  18,980,  in  terms  of  both  the  Maya  notation  and  our  own.  These 
will  be  found  sufficient  to  cover  most  numbers. 

Applying  the  above  rule  to  the  number  31,741,  which  was  selected 
for  our  first  example,  it  is  seen  by  Table  XVI  that  1  Calendar  Round, 
or  18,980  days,  may  be  deducted  from  it;  31,741-18,980  =  12,761. 
In  other  words,  we  can  count  the  number  12,761  forward  (or  back- 
ward had  the  count  been  backward  in  our  exampk)  from  the  starting 
point  4  Aliau  8  Cumhu,  and  reach  exactly  the  same  terminal  date  as 
though  we  had  counted  forward  31,741,  as  in  the  first  case. 

Mathematical  proof  of  this  point  follows : 

12,761    13  =  981 1%    12,761    20  =  638^    12,761    365  =  34||i 

The  numerators  of  the  fractions  in  these  three  quotients  are  8,  1, 
and  351;  these  are  identical  with  the  numerators  of  the  fractions  in 
the  quotients  obtained  by  dividing  31,741  by  the  same  divisors,  those 
indicated  in  rules  1,  2,  and  3,  respectively.  Consequently,  if  these 
three  numerators  be  counted  forw&rd  from  the  corresponding  parts 
of  the  starting  point,  4  Ahau  8  Cumhu,  the  resulting  terms  together 
will  form  the  corresponding  parts  of  the  same  terminal  date,  12  Imix 
14  Kayab. 

Similarly  it  could  be  shown  that  50,721  or  69,701  counted  forward 
or  backward  from  any  starting  point  would  both  reach  this  same  ter- 
minal date,  since  subtracting  2  Calendar  Rounds,  37,960  (see  Table 
XVI),  from  the  first,  and  3  Calendar  Rounds,  56,940  (see  Table  XVI), 
from  the  second,  there  would  remain  in  each  case  12,761 .  The  student 
will  find  his  calculations  greatly  facilitated  if  he  will  apply  this  rule 
whenever  possible.  To  familiarize  the  student  with  the  working  of 
these  rules,  it  is  thought  best  to  give  several  additional  examples 
involving  their  use. 


144 


BUREAU  OF  AMEEICAN  ETHNOLOGY 


[BULL. 


57 


Table  XVI.  80  CALENDAR  ROUNDS  EXPRESSED  IN  ARABIC  AND 

MAYA  NOTATION 


Calendar 
Rounds 

Days 

Cycles,  etc. 

Calendar 
Rounds 

Days 

Cycles,  etc. 

1 

18,  980 

2. 12. 13.  0 

41 

778, 180 

5.  8.  1. 11.  0 

2 

37,  960 

5.  5.  8.0 

42 

797, 160 

5. 10. 14.  6.  0 

3 

56,  940 

7.  ]8.  3.0 

43 

816, 140 

5. 13.  7.  1. 0 

4 

75,  920 

10. 10. 16.  0 

44 

835, 120 

5. 15. 19. 14. 0 

5 

94,  900 

13.  3. 11.  0 

45 

854, 100 

5. 18. 12.  9. 0 

6 

113,  880 

15.36.  6.0 

46 

873, 080 

6.  1.  5.  4.0 

7 

132,  860 

18.  9.  1.0 

47 

892,  060 

6.  3. 17. 17. 0 

8 

151,  840 

1.  1.  1. 14.  0 

48 

911,  040 

6.  6. 10. 12.  0 

9 

170,  820 

1.  3. 14.  9.  0 

49 

930,  020 

6.  9.  3.  7.0 

10 

189,  800 

1.  6.  7.  4.0 

50 

949,  000 

6. 11. 16.  2. 0 

11 

208,  780 

1.  8. 19. 17.  0 

51 

967,  980 

6. 14.  8. 15. 0 

12 

227,  760 

1. 11. 12. 12.  0 

52 

986,  960 

6. 17.  1. 10. 0 

13 

246,  740 

1. 14.  5.  7.  0 

53 

1, 005,  940 

6. 19. 14.  5. 0 

14 

265,  720 

1. 16. 18.  2.  0 

54 

1,  024,  920 

7.  2.  7.  0.0 

15 

284, 700 

1. 19. 10. 15.  0 

55 

1,  043,  900 

7.  4. 19. 13. 0 

16 

303,  680 

2.  2.  3. 10.  0 

56 

1,  062,  880 

7.  7.12.  8.0 

17 

322,  660 

2.  4. 16.  5.  0 

57 

1, 081,  860 

7. 10.  5.  3. 0 

18 

341,  640 

2.  7.  9.  0. 0 

58 

1, 100,  840 

7. 12. 17. 16.  0 

19 

360,  620 

2. 10.  1. 13.  0 

59 

1, 119,  820 

7. 15. 10. 11.  0 

20 

379, 600 

2. 12. 14.  8.  0 

60 

1, 138,  800 

7. 18.  3.  6.  0 

21 

398, 580 

2. 15.  7.  3.  0 

61 

•1, 157,  780 

8.  0. 16.  1. 0 

22 

417,  560 

2. 17. 19. 16.  0 

62 

1, 176,  760 

8.  3.  8. 14, 0 

23 

436,  540 

3.  0. 12. 11.  0 

63 

1, 195,  740 

8.  6.  1.  9. 0 

24 

455,  520 

3.  3.  5.  6.0 

64 

1,  214,  720 

8.  8. 14.  4.  0 

25 

474, 500 

3.  5. 18.  1.  0 

65 

1,  233,  700 

8. 11.  6. 17.  0 

26 

493, 480 

3.  8. 10. 14.  0 

66 

1,  252,  680 

8. 13. 19. 12.  0 

27 

512,  460 

3. 11.  3.  9.  0 

67 

1,  271,  660 

8. 16. 12.  7.  0 

28 

531,  440 

3. 13. 16.  4.  0 

68 

1,  290,  640 

8. 19.  5.  2.  0 

29 

550, 420 

3. 16.  8. 17.  0 

69 

1,  309,  620 

9.  1. 17. 15.  0 

30 

569, 400 

3. 19.  1. 12.  0 

70 

1,  328,  600 

9.  4. 10. 10.  0 

31 

588,  380 

4.  1. 14.  7.  0 

71 

1,  347,  580 

9.  7.  3.  5.0 

32 

607, 360 

4.  4.  7.  2.0 

72 

1,  366,  560 

9.  9.16.  0.0 

33 

626, 340 

4.  6. 19. 15.  0 

73 

1,  385,  540 

9. 12.  8. 13.  0 

34 

645,320 

4.  9. 12. 10.  0 

74 

1,  404,  520 

9.15.  1.  8.0 

35 

664, 300 

4.12.  5.  5.0 

75 

1,  423,  500 

9.17.14.  3.0 

36 

683, 280 

4.14.18.  0.0 

76 

1,442, 480 

10.  0.  6.16.0 

37 

702, 260 

4. 17. 10. 13.  0 

77 

1, 461,  460 

10.  2. 19.  ILO 

38 

721,  240 

5.  0.  3.  8.0 

78 

1,  480, 440 

10.  5.12.  6.0 

39 

740, 220 

5.  2.16.  3.0 

79 

1,  499,  420 

10.  8.  5.  LO 

40 

759,  200 

5.  5.  8.16.0 

80 

1,518,400 

10. 10. 17. 14.  0 

MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEEOGLYPHS  145 

Let  US  count  forward  the  number  5,799  from  the  starting  point 
2  Kan  7  Tzec.  It  is  apparent  at  the  outset  that,  since  this  number 
is  less  than  18,980,  or  1  Calendar  Round,  the  preliminary  rule  given 
on  page  143  does  not  apply  in  this  case.  Therefore  we  may  proceed 
with  the  first  rule  given  on  page  139,  by  means  of  which  the  new  day 
coefficient  may  be  determined.  Dividing  the  given  number  by  13 
we  have :  5,799  13  =  446  ^ig-.  Counting  forward  the  numerator  of  the 
fractional  part  of  the  resulting  quotient  (1)  from  the  day  coefficient 
of  the  starting  point  (2),  we  reach  3  as  the  day  coefficient  of  the 
terminal  date. 

The  second  rule  given  on  page  140  tells  how  to  find  the  day  sign  of 
the  terminal  date.  Dividing  the  given  number  by  20,  we  have: 
5,799^  20  =  289it.  Counting  forward  the  numerator  of  the  frac- 
tional part  of  the  resulting  quotient  (19)  from  the  day  sign  of  the 
starting  point,  Kan,  in  the  sequence  of  the  twenty-day  signs  given 
in  Table  I,  the  day  sign  Akbal  will  be  reached,  which  will  be  the 
day  sign  of  the  terminal  date.  Therefore  the  day  of  the  terminal 
date  will  be  3  Akbal. 

The  third  rule,  given  on  page  141,  tells  how  to  find  the  position 
which  the  day  of  the  terminal  date  occupied  in  the  365-day  year. 
Dividing  the  given  number  by  365,  we  have:  5,799 -^ 365  =  15|f|. 
Counting  forward  the  numerator  of  the  fractional  part  of  the  resulting 
quotient,  324,  from  the  year  position  of  the  starting  date,  7  Tzec,  in 
the  sequence  of  the  365  year  positions  given  in  Table  XV,  the  position 
6  Zip  will  be  reached  as  the  position  in  the  year  of  the  day  of  the 
terminal  date.  The  count  by  means  of  which  the  position  6  Zip  is 
determined  is  given  in  detail.  After  the  year  position  of  the  starting 
point,  7  Tzec,  it  requires  12  more  positions  (Nos.  8-19,  inclusive) 
before  the  close  of  that  month  (see  Table  XV)  will  be  reached.  And 
after  the  close  of  Tzec,  13  uinals  and  the  xma  kaba  kin  must  pass 
before  the  end  of  the  year;  13x20  +  5  =  265,  and  265  +  12  =  277. 
This  latter  number  subtracted  from  324,  the  total  number  of  posi- 
tions to  be  counted  forward,  will  give  the  number  of  positions  which 
remain  to  be  counted  in  the  next  year  following:  324  —  277  =  47. 
Counting  forward  47  in  the  new  year,  we  find  that  it  will  use  up  the 
>  months  Pop  and  Uo  (20  +  20=40)  and  extend  7  positions  into  the 
month  Zip,  or  to  6  Zip.  Therefore,  gathering  together  the  values 
determined  for  the  several  parts  of  the  terminal  date,  we  may  say 
that  in  counting  forward  5,799  from  the  starting  point  2  Kan  7  Tzec, 
the  terminal  date  reached  will  be  3  Akbal  6  Zip. 

For  the  next  example  let  us  select  a  much  higher  number,  say 
322,920,  which  we  will  assume  is  to  be  counted  forward  from  the 
starting  point  13  Ik  0  Zip.  Since  this  number  is  above  18,980,  we 
may  apply  our  preliminary  rule  (p.  143)  and  deduct  all  the  Calendar 
43508°— Bull.  57—15  10 


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Rounds  possible.  By  turning  to  Table  XVI  we  see  that  17  Calendar 
Rounds,  or  322,660,  may  be  deducted  from  our  number:  322,920- 
322,660  =  260.  In  other  words,  we  can  use  260  exactly  as  though  it 
were  322,920.  Dividing  by  13,  we  have  260-^13  =  20.  Since  there 
is  no  fraction  in  the  quotient,  the  numerator  of  the  fraction  will  be 
0,  and  coimting  0  forward  from  the  day  coefficient  of  the  starting 
point,  13,  we  have  13  as  the  day  coefficient  of  the  terminal  date 
(rule  1,  p.  139).  Dividing  by  20  we  have  260-^20  =  13.  Since  there 
is  no  fraction  in  the  quotient,  the  numerator  of  the  fraction  will  be 
0,  and  counting  forward  0  from  the  day  sign  of  the  starting  point,  Ik 
in  Table  I,  the  day  sign  Ik  will  remain  the  day  sign  of  the  terminal 
date  (rule  2,  p.  140).  Combining  the  two  values  just  determined, 
we  see  that  the  day  of  the  terminal  date  will  be  13  Ik,  or  a  day  of  the 
same  name  as  the  day  of  the  starting  point.  This  follows  also  from 
the  fact  that  there  are  only  260  differently  named  days  (see  pp.  41-44) 
and  any  given  day  will  have  to  recur,  therefore,  after  the  lapse 
of  260  days.i  Dividing  by  365  we  have:  260 -J- 365  =  Counting 
forward  the  numerator  of  the  fraction,  260,  from  the  year  position  of 
the  starting  point,  0  Zip,  in  Table  XV,  the  position  in  the  year  of  the 
day  of  the  terminal  date  will  be  found  to  be  0  Pax.  Since  260  days 
equal  just  13  uinals,  we  have  only  to  count  forward  from  0  Zip  13 
uinals  in  order  to  reach  the  year  position;  that  is,  0  Zotz  is  1  uinal; 
to  0  Tzec  2  uinals,  to  0  Xul  3  uinals,  and  so  on  in  Table  XV  to  0  Pax, 
which  will  complete  the  last  of  the  13  uinals  (rule  3,  p.  141). 

Combining  the  above  values,  we  find  that  in  counting  forward 
322,920  (or  260)  from  the  starting  point  13  Ik  0  Zip,  the  terminal 
date  reached  is  13  Ik  0  Pax. 

In  order  to  illustrate  the  method  of  procedure  when  the  count  is 
backward,  let  us  assume  an  example  of  this  kind.  Suppose  we  count 
backward  the  number  9,663  from  the  starting  point  3  Imix  4  Uayeb. 
Since  this  number  is  below  18,980,  no  Calendar  Round  can  be  deducted 
from  it.  Dividing  the  given  number  by  13,  we  have:  9,663 -^  13  = 
743-^.  Counting  the  numerator  of  the  fractional  part  of  this  quo- 
tient, 4,  hackward  from  the  day  coefficient  of  the  starting  point,  3, 
we  reach  12  as  the  day  coefiicient  of  the  terminal  date,  that  is,  2,  1, 
13,  12  (rule  1,  p.  139).  Dividing  the  given  number  by  20,  we  have: 
9,663^20=4832%.  Counting  the  numerator  of  the  fractional  part 
of  this  quotient,  3,  hackward  from  the  day  sign  of  the  starting  point, 
Imix,  in  Table  I,  we  reach  Eznab  as  the  day  sign  of  the  terminal 
date  (Ahau,  Cauac,  Eznab);  consequently  the  day  reached  in  the 
count  will  be  12  Eznab.    Dividing  the  given  number  by  365,  we  have 

1  The  student  can  prove  this  point  for  himself  by  tiiming  to  the  tonalamatl  wheel  in  pi.  5;  after  selecting 
any  particular  day,  as  1  Ik  for  example,  proceed  to  coxuit  260  days  from  this  'day  as  a  starting  point,  in 
either  direction  around  the  wheel.  No  matter  in  which  direction  he  has  (?0UJ:ited,  whether  begirming 
with  13  Imix  or  2  Akbal,  the  260th  day  will  be  I  Ik  again, 


MORLEY]      INTRODUCTION  TO  STUDY  Oi   MAYA  HIEROGLYPHS 


147 


9,663 -j- 365  =  Counting  backward  the  numerator  of  the  frac- 

tional part  of  this  quotient,  173,  from  the  year  position  of  the  starting 
point,  4  TJayeb,  the  year  position  of  the  terminal  date  will  be  found  to 
be  11  Yax.  Before  position  4  Uayeb  (see  Table  XV)  there  are  4 
positions  in  that  division  of  the  year  (3,2, 1,0).  Coimting  these  hack- 
ward  to  the  end  of  the  month  Cumhu  (see  Table  XV),  we  have  left 
169  positions  (173—4  =  169);  this  equals  8  uinals  and  9  days  extra. 
Therefore,  beginning  with  the  end  of  Cumliu,  we  may  count  backward 
8  whole  uinals,  namely:  Cumliu,  Kayab,  Pax,  Muan,  Kankin,  Mac, 
Ceh,  and  Zac,  which  will  bring  us  to  the  end  of  Yax  (since  we  are 
counting  backward).  As  we  have  left  still  9  days  out  of  our  original 
173,  these  must  be  counted  backward  from  position  0  Zac,  that  is, 
beginning  with  position  19  Yax:  1^,  18,  17,  16,  15,  14,  13,  12,  11;  so 
11  Yax  is  the  position  in  the  year  of  the  day  of  the  terminal  date. 
Assembling  the  above  values,  we  find  that  in  counting  the  number 
9,663  backward  from  the  starting  point,  2  Imix  4  Uayeb,  the  terminal 
date  is  12  Eznab  11  Yax.  Whether  the  count  be  forward  or  back- 
ward, the  method  is  the  same,  the  only  difference  being  in  the  direc- 
tion of  the  counting. 

This  concludes  the  discussion  of  the  actual  arithmetical  processes 
involved  in  counting  forward  or  backward  any  given  number  from 
any  given  date;  however,  before  explaining  the  fifth  and  final  step 
in  deciphering  the  Maya  numbers,  it  is  first  necessary  to  show  how 
this  method  of  counting  was  applied  to  the  Long  Count. 

The  numbers  used  above  in  connection  with  dates  merely  express 
the  difference  in  time  between  starting  points  and  terminal  dates, 
without  assigning  either  set  of  dates  to  their  proper  positions  in  Maya 
chronology ;  that  is ,  in  the  Long  Count.  Consequently,  since  any  Maya 
date  recurred  at  successive  intervals  of  52  years,  by  the  time  their 
historic  period  had  been  reached,  more  than  3,000  years  after  the 
starting  point  of  their  chronology,  the  Maya  had  upward  of  70  dis- 
tinct dates  of  exactly  the  same  name  to  distinguish  from  one  another. 

It  was  stated  on  page  61  that  the  0,  or  starting  point  of  Maya 
chronology,  was  the  date  4  Aliau  8  Cumliu,  from  which  all  subsequent 
dates  were  reckoned;  and  further,  on  page  63,  that  by  recording  the 
number  of  cycles,  katuns,  tuns,  uinals,  and  kins  which  had  elapsed 
in  each  case  between  this  date  and  any  subsequent  dates  in  the  Long 
Count,  subsequent  dates  of  the  same  name  could  be  readily  distin- 
guished from  one  another  and  assigned  at  the  same  time  to  their 
proper  positions  in  Maya  chronology.  This  method  of  fixing  a  date 
in  the  Long  Count  has  been  designated  Initial-series  dating. 

The  generally  accepted  method  of  writing  Initial  Series  is  as  follows: 
9.0.0.0.0.    8  Ahau  13  Ceh 
The  particular  Initial-Series  written  here  is  to  be  interpreted  thus: 
'Counting  forward  9  cycles ,  0  katuns j  0  tuns,  0  uinals,  and  0  kins 


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from  4  Ahau  8  Cumhu,  the  starting  point  of  Maya  chronology  (always 
unexpressed  in  Initial  Series),  the  terminal  date  reached  will  be  8 
Ahau  13  Ceh."  ^    Or  again: 

9.14.13.4.17.    12  Caban  5  Kayab 
This  Inital  Series  reads  thus:    Counting  forward  9  cycles,  14  katuns, 
13  tuns,  4  uinals,  and  17  kins  from  4  Ahau  8  Cumhu,  the  starting 
point  of  Maya  chronology  (unexpressed),  the  terminal  date  reached 
mil  be  12  Caban  5  Kayab." 

The  time  which  separates  any  date  from  4  Ahau  8  Cumhu  may 
be  called  that  date's  Initial-series  value.  For  example,  in  the  first 
of  the  above  cases  the  number  9.0.0.0.0  is  the  Initial-series  value  of 
the  date  8  Ahau  13  Ceh,  and  in  the  second  the  number  9.14.13.4.17 
is  the  Initial-series  value  of  the  date  12  Caban  6  Kayab.  It  is  clear 
from  the  foregoing  that  although  the  date  8  Ahau  13  Ceh,  for  example, 
had  recurred  upward  of  70  times  since  the  beginning  of  their  chro- 
nology, the  Maya  were  able  to  distinguish  any  particular  8  Ahau  13  Ceh 
from  all  the  others  merely  by  recording  its  distance  irom  the  starting 
point;  in  other  words,  giving  thereto  its  particular  Initial-series 
value,  as  9.0.0.0.0.  in  the  present  case.  Similarly,  any  particular  12 
Caban  5  Kayab,  by  the  addition  of  its  corresponding  Initial-series 
value,  as  9.14.13.4.17  in  the  case  above  cited,  was  absolutely  fixed 
in  the  Long  Count — that  is,  in  a  period  of  374,400  years. 

Keturning  now  to  the  question  of  how  the  counting  of  numbers  was 
applied  to  the  Long  Count,  it  is  evident  that  every  date  in  Maya 
chronology,  starting  points  as  well  as  terminal  dates,  Tiad  its  own  par- 
ticular Initial-series  value,  though  in  many  cases  these  values  are  not 
recorded.  However,  in  most  of  the  cases  in  which  the  Initial-series 
values  of  dates  are  not  recorded,  they  may  be  calculated  by  means 
of  their  distances  from  other  dates,  whose  Initial-series  values  are 
known.  This  adding  and  subtracting  of  numbers  to  and  from  Initial 
Series  ^  constitutes  the  application  of  the  above-described  arithmetical 
processes  to  the  Long  Count.  Several  examples  of  this  use  are  given 
below. 

Let  us  assume  for  the  first  case  that  the  number  2.5.6.1  is  to  be 
counted  forward  from  the  Initial  Series  9.0.0.0.0  8  Ahau  13  Ceh.  By 
multiplying  the  values  of  the  katuns,  tuns,  uinals,  and  kins  given  in 
Table  XIII  by  their  corresponding  coefiicients,  in  this  case  2,  5,  6, 
and  1,  respectively,  and  adding  the  resulting  products  together,  we 
find  that  2.5.6.1  reduces  to  16,321  units  of  the  first  order. 

Counting  this  forward  from  8  Ahau  13  Ceh  as  indicated  by  the  rules 
on  pages  138-143,  the  terminal  date  1  Imix  9  Yaxkin  will  be  reached. 

1  The  student  may  prove  this  for  himself  by  reducing  9.0.0.0.0  to  days  (1,296,000),  and  counting  forward 
this  number  from  the  date  4  Ahau  8  Cumhu,  as  described  in  the  rules  on  pages  138-143.  The  terminal 
date  reached  will  be  8  Ahau  13  Ceh,  as  given  above. 

2  Numbers  may  also  be  added  to  or  subtracted  from  Period-ending  dates,  since  the  positions  of  such  dates 
are  also  fixed  in  the  Long  Count,  and  consequently  may  be  used  as  bases  of  reference  for  dates  whose  posi- 
tions in  the  Long  Coimt  are  not  recorded. 


MORLEY]      INTEODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


149 


Moreover,  since  the  Initial-series  value  of  the  starting  point  8  Ahau 
13  Ceh  was  9.0.0.0.0,  the  Initial-series  value  of  1  Imix  9  Yaxkin,  the 
terminal  date,  may  be  calculated  by  adding  its  distance  from  8  Ahau 
13  Ceh  to  the  Initial-series  value  of  that  date: 

9.0.0.0.0  (Initial-series  value  of  starting  point)  8  Ahau  13  Ceh 

2.5.6.1  (distance  from  8  Ahau  13  Ceh  to  1  Imix  9  Yaxkin) 
9.2.5.6.1  (Initial -series  value  of  terminal  date)  1  Imix  9  Yaxkin 

That  is,  by  calculation  we  have  determined  the  Initial-series  value 
of  the  particular  1  Imix  9  Yaxkin,  which  was  distant  2.5.6.1  from 
9,0.0.0.0  8  Ahau  13  Ceh,  to  be  9.2.5.6.1,  notwithstanding  that  this 
fact  was  not  recorded. 

The  student  may  prove  the  accuracy  of  this  calcula  bion  by  treating 
9.2.5.6.1  1  Imix  9  Yaxkin  as  a  new  Initial  Series  and  counting  forward 
9.2.5.6.1  from  4  Ahau  8  Cumhu,  the  starting  point  of  all  Initial  Series 
known  except  two.  If  our  calculations  are  correct,  the  former  date 
will  be  reached  just  as  if  we  had  counted  forward  only  2.5.6.1  from 
9.0.0.0.0  8  Ahau  13  Ceh. 

In  the  above  example  the  distance  number  2.5.6.1  and  the  date 
1  Imix  9  Yaxkin  to  which  it  reaches,  together  are  called  a  Secondary 
Series.  This  method  of  dating  already  described  (see  pp.  74-76  et  seq. ) 
seems  to  have  been  used  to  avoid  the  repetition  of  the  Initial-series 
values  for  all  the  dates  in  an  inscription.  For  example,  in  the  accom- 
panying text — 

9.12.  2.  0.16  5  Cib  14  Yaxkin 

12.  9.15 

[9.12.14.10.11]  1  9  Chuen  9  Kankin 

5 

[9.12.14.10.16]  1  Cib  14  Kankin 

1.  0.  2.  5 
[9.13.14.13.  1]  5  Imix  19  Zac 

1  In  adding  two  Maya  numbers,  for  example  9.12.2.0.16  and  12.9.5,  oare  should  be  taken  first  to  arrange 
like  units  under  like,  as: 

9.12.  2.  0.16 
12.  9.  5 


9.12.14.10.  1 

Next,  beginning  at  the  right,  the  kins  or  units  of  the  1st  place  are  added  together,  and  after  all  the  20s 
(here  1)  have  been  deducted  from  this  sum,  place  the  remainder  (here  1)  in  the  kin  place.  Next  add  the 
uinals,  or  units  of  the  2d  place,  adding  to  them  1  for  each  20  which  was  carried  forward  from  the  1st  place. 
After  all  the  18s  possible  have  been  deducted  from  this  sum  (here  0)  place  the  remainder  (here  10)  in  the 
uinal  place.  Next  add  the  tuns,  or  units  of  the  3d  place,  adding  to  them  1  for  each  18  which  was  carried 
forward  from  the  2d  place,  and  after  deducting  all  the  20s  possible  (here  0)  place  the  remainder  (here  14) 
in  the  tun  place.  Proceed  in  this  manner  until  the  highest  units  present  have  been  added  and  written 
below. 

Subtraction  is  just  the  reverse  of  the  preceding.   Using  the  same  numbers: 

9.12.  2.0.16 
12.9.  5 


9.11.  9.9.11 

5  kins  from  16=  11;  9  uinals  from  18  uinals  (1  tun  has  to  be  borrowed)=9;  12  tuns  from  21  tuns  (1  katun  has 
to  be  borrowed,  which,  added  to  the  1  tun  left  in  the  minuend,  makes  21  tuns)=9  tuns;  0  katuns  from 
11  katuns  (1  katun  having  been  borrowed)=  11  katuns;  and  0  cycles  from  9  cycles=9  cycles. 


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[BULL.  57 


the  only  parts  actually  recorded  are  the  Initial  Series  9.12.2.0.16 
5  Cib  14  Yaxkin,  and  the  Secondary  Series  12.9.15  leading  to  9  Chuen 

9  Kankin ;  the  Secondary  Series  5  leading  to  1  Cib  14  Kankin ;  and 
the  Secondary  Series  1.0.2.5  leading  to  6  Imix  19  Zac.  The  Initial- 
series  values:  9.12.14.10.11;  9.12.14.10.16;  and  9.13.14.13.1,  belong- 
ing to  the  three  dates  of  the  Secondary  Series,  respectively,  do  not 
appear  in  the  text  at  all  (a  fact  indicated  by  the  brackets),  but 
are  found  only  by  calculation.  Moreover,  the  -  student  should  note 
that  in  a  succession  of  interdependent  series  like  the  ones  just  given 
the  terminal  date  reached  by  one  number,  as  9  Chuen  9  Kankin, 
becomes  the  starting  point  for  the  next  number,  5.  Again,  the  ter- 
minal date  reached  by  counting  5  from  9  Chuen  9  Kankin,  that  is, 
1  Cib  14  Kankin,  becomes  the  starting  point  from  which  the  next 
number,  1.0.2.5,  is  counted.  In  other  words,  these  terms  are  only 
relative,  since  the  terminal  date  of  one  number  will  be  the  starting 
point  of  the  next. 

Let  us  assume  for  the  next  example  that  the  number  3.2  is  to  be 
counted  forward  from  the  Initial  Series  9.12.3.14.0  6  Ahau  8  TJo. 
Reducing  3  uinals  and  2  kins  to  kins,  we  have  62  units  of  the  first 
order.  Counting  forward  62  from  6  Ahau  8  ITo,  as  indicated  by  the 
rules  on  pages  138-143,  it  is  found  that  the  terminal  date  will  be  2  Ik 

10  Tzec.  Since  the  Initial-series  value  of  the  starting  point  6  Ahau 
8  Uo  is  known,  namely,  9.12.3.14.0,  the  Initial  Series  corresponding 
to  the  terminal  date  may  be  calculated  from  it  as  before: 

9.12.3.14.0  (Initial-series  value  of  the  starting  point)  6  Ahau  8  TJo 
3.2   (distance  from  5  Ahau  8  Uo  forward  to  2  Ik  10  Tzec) 
[9.12.3.17.2]  (Initial-series  value  of  tho  terminal  date)  2  Ik  10  Tzec 

The  bracketed  9.12.3.17.2  in  the  Initial-series  value  corresponding 
to  the  date  2  Ik  10  Tzec  does  not  appear  in  the  record  but  was  reached 
by  calculation.  The  student  may  prove  the  accuracy  of  this  result 
by  treating  9.12.3.17.2  2  Ik  10  Tzec  as  a  new  Initial  Series,  and 
counting  forward  9.12.3.17.2  from  4  Ahau  8  Cumhu  (the  starting 
point  of  Maya  chronology,  unexpressed  in  Initial  Series).  If  our 
calculations  are  correct,  the  same  date,  2  Ik  10  Tzec,  will  be  reached, 
as  though  we  had  counted  only  3.2  forward  from  the  Initial  Series 
9.12.3.14.0  5  Ahau  8  Uo. 

One  more  example  presenting  a  backward  count"  will  suffice  to 
illustrate  this  method.  Let  us  count  the  number  14.13.4.17  backward 
from  the  Initial  Series  9.14.13.4.17  12  Caban  6  Kayab.  Reducing 
14.13.4.17  to  units  of  the  1st  order,  we  have  105,577.  Counting  this 
number  hacJcward  from  12  Caban  6  Kayab,  as  indicated  in  the  rules 
on  pages  138-143,  we  find  that  the  terminal  date  will  be  8  Ahau  13  Ceh. 
Moreover,  since  the  Initial-series  value  of  the  starting  point  12  Caban 
5  Kayab  is  known,  namely,  9.14.13.4.17,  the  Initial-series  value  of 


MORLBY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  151 


the  terminal  date  may  be  calculated  by  subtracting  the  distance  num- 
ber 14.13.4.17  from  the  Initial  Series  of  the  starting  point: 

9.14.13.4.17  (Initial-series  value  of  the  starting  point)  12  Caban  5 
Kayab 

14.13.4.17  (distance  from  12  Caban  5  Kayab  backward  to  8  Ahau 
13  Geh) 

[9.  0.  0.0.  0]  (Initial-series  value  of  the  terminal  date)  8  Ahau  13 
Ceh 

The  bracketed  parts  are  not  expressed.  We  have  seen  elsewhere 
that  the  Initial  Series  9.0,0.0.0  has  for  its  terminal  date  8  Abau  13  Ceh ; 
therefore  our  calculation  proves  itself. 

The  foregoing  examples  make  it  sufficiently  clear  that  the  distance 
numbers  of  Secondary  Series  may  be  used  to  determine  the  Initial- 
series  values  of  Secondary-series  dates,  either  by  their  addition  to 
or  subtraction  from  known  Initial-series  dates. 

We  have  come  now  to  the  final  step  in  the  consideration  of  Maya 
numbers,  namely,  the  identification  of  the  terminal  dates  determined 
"  by  the  calculations  given  under  the  fourth  step,  pages  138-143.  This 
step  may  be  summed  up  as  follows : 

Fifth  Step  in  Solving  Maya  Numbers 

Find  the  terminal  date  to  which  the  number  leads. 

As  explained  under  the  fourth  step  (pp.  138-143),  the  terminal  date 
may  be  found  by  calculation.  The  above  direction,  however,  refers 
to  the  actual  finding  of  the  terminal  dates  in  the  texts;  that  is,  where 
to  look  for  them.  It  may  be  said  at  the  outset  in  this  connection 
that  terminal  dates  in  the  great  majority  of  cases  follow  immediately 
the  numbers  which  lead  to  them.  Indeed,  the  connection  between 
distance  numbers  and  their  corresponding  terminal  dates  is  far  closer 
than  between  distance  numbers  and  their  corresponding  starting 
points.  This  probably  results  from  the  fact  that  the  closing  dates 
of  Maya  periods  were  of  far  more  importance  than  their  opening 
dates.  Time  was  measured  by  elapsed  periods  and  recorded  in  terms 
of  the  ending  days  of  such  periods.  The  great  emphasis  on  the  clos- 
ing date  of  a  period  in  comparison  with  its  opening  date  probably 
caused  the  suppression  and  omission  of  the  date  4  Ahau  8  Cumhu, 
the  starting  point  of  Maya  chronology,  in  all  Initial  Series.  To  the 
same  cause  also  may  probably  be  attributed  the  great  uniformity  in 
the  positions  of  almost  all  terminal  dates,  i.  e.,  immediately  after  the 
numbers  leading  to  them. 

We  may  formulate,  therefore,  the  following  general  rule,  which  the 
student  will  do  well  to  apply  in  every  case,  since  exceptions  to  it  arc 
verv  rare : 

Rule.  The  terminal  date  reached  by  a  number  or  series  almost 
invariably  follows  immediately  the  last  term  of  the  number  or  series 
leading  to  it. 


152 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


This  applies  equally  to  all  terminal  dates,  whether  in  Initial  Series, 
Secondary  Series,  Calendar-round  dating  or  Period-ending  dating, 
though  in  the  case  of  Initial  Series  a  peculiar  division  or  partition  of 
the  terminal  date  is  to  be  noted. 

Throughout  the  inscriptions,  excepting  in  the  case  of  Initial  Series, 
the  month  parts  of  the  dates  almost  invariably  follow  immediately 
the  days  whose  positions  in  the  year  they  designate,  without  any 
other  glyphs  standing  between;  as,  for  example,  8  Ahau  13  Ceh, 
12  Gaban  5  Kayab,  etc.  In  Initial  vSeries,  on  the  other  hand,  the 
da,y  parts  of  the  dates,  as  8  Ahau  and  12  Caban,  in  the  above  exam- 
ples, are  almost  invariably  separated  from  their  corresponding 
month  parts,  13  Ceh  or  5  Kayab,  by  several  intervening  glyphs. 
The  positions  of  the  day  parts  in  Initial-series  terminal  dates  are 
quite  regular  according  to  the  terms  of  the  above  rule;  that  is,  they 
follow  immediately  the  lowest  period  of  the  number  which  in  each 
case  shows  their  distance  from  the  unexpressed  starting  point,  4  Ahau 
8  Cumhu.  The  positions  of  the  corresponding  month  parts  are,  on 
the  other  hand,  irregular.  These,  instead  of  standing  immediately  - 
after  the  days  whose  positions  in  the  year  they  designate,  follow  at 
the  close  of  some  six  or  seven  intervening  glyphs.  These  intervening 
glyphs  have  been  called  the  Supplementary  Series,  though  the  count 
which  they  record  has  not  as  yet  been  deciphered.^  The  month  glyph 
in  the  great  majority  of  cases  follows  immediately  the  closing  ^  glyph 
of  the  Supplementary  Series.  The  form  of  this  latter  sign  is  always 
unmistakable  (see  fig.  65),  and  it  is  further  characterized  by  its 
numerical  coefficient,  which  can  never  be  anything  but  9  or  10.^  See 
examples  of  this  sign  in  the  figure  just  mentioned,  where  both  nor- 
mal forms  a,  c,  e,  g,  and  Ji  and  head  variants  h,  d,  and  /  are  included. 

The  student  will  find  this  glyph  exceedingly  helpful  in  locating  the 
month  parts  of  Initial-series  terminal  dates  in  the  inscriptions.  For 
example,  let  us  suppose  in  deciphering  the  Initial  Series  9.16.5.0.0 
8  Ahau  8  Zotz  that  the  number  9.16.5.0.0  has  been  counted  forward 

1  The  Supplementary  Series  present  perhaps  the  most  promising  field  for  future  study  and  investigation 
in  the  Maya  texts.  They  clearly  have  to  do  with  a  numerical  covmt  of  some  kind,  which  of  itself  should 
greatly  facilitate  progress  in  their  interpretation.  Mr.  Goodman  (1S97:  p.  118)  has  suggested  that  in  some 
way  the  Supplementary  Series  record  the  dates  of  the  Initial  Series  they  accompany  according  to  some 
other  and  unknown  method,  though  he  ofEers  no  proof  in  support  of  this  hypothesis.  Mr.  Bowditch 
(1910:  p.  244)  believes  they  probably  relate  to  time,  because  the  glyphs  of  which  they  are  composed  have 
numbers  attached  to  them.  He  has  suggested  the  name  Supplementary  Series  by  which  they  are  known, 
implying  in  the  designation  that  these  Series  in  some  way  supplement  or  complete  the  meaning  of  the 
Initial  Series  with  wliich  they  are  so  closely  connected.  The  writer  believes  that  they  treat  of  some 
lunar  count.  It  seems  almost  certain  that  the  moon  glyph  occurs  repeatedly  in  the  Supplementary 
Series  (see  fig.  65). 

2  The  word  "closing"  as  used  here  means  only  that  in  reading  from  left  to  right  and  from  top  to  bottom- 
that  is,  in  the  normal  order— the  sign  shown  in  fig.  65  is  always  the  last  one  in  the  Supplementary  Series, 
usually  standing  immediately  before  the  month  glyph  of  the  Initial-series  terminal  date.  It  does  not 
signify,  however,  that  the  Supplementary  Series  were  to  be  read  in  this  direction,  and,  indeed,  there  are 
strong  indications  that  they  followed  the  reverse  order,  from  right  to  left  and  bottom  to  top. 

3  In  a  few  cases  the  sign  shown  in  fig.  65  occurs  elsewhere  in  the  Supplementary  Series  than  as  its  "closing  " 
glyph.  In  such  cases  its  coefficient  is  not  restricted  to  the  number  9  or  10. 


morlet]      introduction  TO  STUDY  OF  MAYA  HIEROGLYPHS  153 


from  4  Ahau  8  Cumhu  (the  unexpressed  starting  point),  and  has  been 
found  by  calculation  to  reach  the  terminal  date  8  Ahau  8  Zotz ;  and 
further,  let  us  suppose  that  on  inspecting  the  text  the  day  part  of 
this  date  (8  Ahau)  has  been  found  to  be  recorded  immediately  after 
the  0  kins  of  the  number  9.16.5.0.0.  Now,  if  the  student  will  follow 
the  next  six  or  seven  glyphs  until  he  finds  one  like  any  of  the  forms 
in  figure  65,  the  glyph  immediately  following  the  latter  sign  will  be 
in  all  probabihty  the  month  part,  8  Zotz  in  the  above  example,  of 
an  Initial-series'  terminal  date.  In  other  words,  although  the 
meaning  of  the  glyph  shown  in  the  last-mentioned  figure  is  unknown, 
it  is  important  for  the  student  to  recognize  its  form,  since  it  is  almost 
invariably  the  ^ indicator"  of  the  month  sign  in  Initial  Series. 
In  all  other  cases  in  the  inscriptions,  including  also  the  exceptions 


.  e  f  g  h 

Fig.  65.   Sign  for  the  "month  indicator":  a,  c,  e,  g,  h,  Normal  forms;  b,  d,  f,  head  variants. 

to  the  above  rule,  that  is,  where  the  month  parts  of  Initial-series  ter- 
minal dates  do  not  immediately  follow  the  closing  glyph  of  the 
Supplementary  Series,  the  month  signs  follow  immediately  the  day 
signs  whose  positions  in  the  year  they  severally  designate. 

In  the  codices  the  month  signs  when  recorded^  usually  foUow 
immediately  the  days  signs  to  which  they  belong.  The  most  notable 
exception  ^  to  this  general  rule  occurs  in  connection  with  the  Venus- 
solar  periods  represented  on  pages  46-50  of  the  Dresden  Codex, 
where  one  set  of  day  signs  is  used  with  three  different  sets  of  month 
signs  to  form  three  different  sets  of  dates.  For  example,  in  one 
place  the  day  2  Ahau  stands  above  three  different  month  signs — 3 
Cumhu,  3  Zotz,  and  13  Yax — with  each  of  which  it  is  used  to  form  a 


1  In  the  codices  frequently  the  month  parts  of  dates  are  omitted  and  starting  points  and  terminal  dates 
ahke  are  expressed  as  days  only;  thus,  2  Ahau,  5  Imix,  7  Kan,  etc.  This  is  nearly  always  the  case  in 
tonalamatls  and  in  certain  series  of  numbers  in  the  Dresden  Codex. 

2  Only  a  very  few  month  signs  seem  to  be  recorded  in  the  Codex  Tro-Cortesiano  and  the  Codex  Pere- 
sianus.   The  Tro-Cortesiano  has  only  one  (p.  73b),  in  which  the  date  13  Ahau  13  Cumhu  is  recorded 

thus(*).   Comparethemonthforminthisdatewithflg.  20,  ^-6'.   Mr.  Gates  (1910:  p.  21) 
O    finds  three  month  signs  in  the  Codex  Peresianus,  on  pp.  4,  7,  and  18  at  4c7,  7c2,  and 

18b4,  respectively.   The  first  of  these  is  16  Zac  (**).   Compare  this  form  with 
fig.  20,  0.   The  second  is  1  Yaxkin  (f).   Compare  this  form  with  fig.  20,  i-j. 
The  third  is  12  Cumhu  (ft);  see  fig.  20,  z-h'. 


m  m 


n 


154 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


different  date — 2  Ahau  3  Cumliu,  2  Ahau  3  Zotz,  and  2  Ahau  13  Yax. 

In  these  pages  the  month  signs,  with  a  few  exceptions,  do  not  follow 
immediately  the  days  to  which  they  belong,  but  on  the  contrary  they 
are  separated  from  them  by  several  intervening  glyphs.  This  abbre- 
viation in  the  record  of  these  dates  was  doubtless  prompted  by  the 
desire  or  necessity  for  economizing  space.  In  the  above  example, 
instead  of  repeating  the  2  Ahau  with  each  of  the  two  lower  month 
signs,  3  Zotz  and  13  Yax,  by  writing  it  once  above  the  upper  month 
sign,  3  Cumhu,  the  scribe  intended  that  it  should  be  used  in  turn 
with  each  one  of  the  three  month  signs  standing  below  it,  to  form  three 
different  dates,  saving  by  this  abbreviation  the  space  of  two  glyphs, 
that  is,  double  the  space  occupied  by  2  Ahau. 

With  the  exception  of  the  Initial-series  dates  in  the  inscriptions 
and  the  Venus-Solar  dates  on  pages  46-50  of  the  Dresden  Codex,  we 
may  say  that  the  regular  position  of  the  month  glyphs  in  Maya  writing 
was  immediately  following  the  day  glyphs  whose  positions  in  the  year 
they  severally  designated. 

In  closing  the  presentation  of  this  last  step  in  the  process  of  deci- 
phering numbers  in  the  texts,  the  great  value  of  the  terminal  date 
as  a  final  check  for  all  the  calculations  involved  under  steps  1-4 
(pp.  134-151)  should  be  pointed  out.  If  after  having  worked  out 
the  terminal  date  of  a  given  number  according  to  these  rules  the  ter- 
minal date  thus  found  should  differ  from  that  actually  recorded  under 
step  5,  we  must  accept  one  of  the  following  alternatives: 

1.  There  is  an  error  in  our  own  calculations;  or 

2.  There  is  an  error  in  the  original  text;  or 

3.  The  case  in  point  lies  without  the  operation  of  our  rules. 
It  is  always  safe  for  the  beginner  to  proceed  on  the  assumption  that 
the  first  of  the  above  alternatives  is  the  cause  of  the  error;  in  other 
words,  that  his  own  calculations  are  at  fault.  If  the  terminal  date  as 
calculated  does  not  agree  with  the  terminal  date  as  recorded,  the 
student  should  repeat  his  calculations  several  times,  checking  up  each 
operation  in  order  to  eliminate  the  possibility  of  a  purely  arithmetical 
error,  as  a  mistake  in  multiplication-  After  all  attempts  to  reach 
the  recorded  terminal  date  by  counting  the  given  number  from  the 
starting  point  have  failed,  the  process  should  be  reversed  and  the 
attempt  made  to  reach  the  starting  point  by  counting  backward  the 
given  number  from  its  recorded  terminal  date.  Sometimes  this 
reverse  process  will  work  out  correctly,  showing  that  there  must  be 
some  arithmetical  error  in  our  original  calculations  which  we  have 
failed  to  detect.  However,  when  both  processes  have  failed  several 
times  to  connect  the  starting  point  with  the  recorded  terminal  date 
by  use  of  the  given  number,  there  remains  the  possibility  that  either 
the  starting  point  or  the  terminal  date,  or  perhaps  both,  do  not 
belong  to  the  given  number.    The  rules  for  determining  this  fact 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  155 

have  been  given  under  step  2,  page  135,  and  step  4,  page  138.  If 
after  applying  these  to  the  case  in  point  it  seems  certain  that  the 
starting  point  and  terminal  date  used  in  the  calculations  both  be- 
long to  the  given  number,  we  have  to  fall  back  on  the  second  of 
the  above  alternatives,  that  is,  that  there  is  an  error  in  the  original 
text. 

Although  very  unusual,  particularly  in  the  inscriptions,  errors  in 
the  original  texts  are  by  no  means  entirely  unknown.  These  seem 
to  be  restricted  chiefly  to  errors  in  numerals,  as  the  record  of  7  for 
8,  or  7  for  12  or  17,  that  is,  the  omission  or  insertion  of  one  or  more 
bars  or  dots.  In  a  very  few  instances  there  seem  to  be  errors  in  the 
month  glyph.  Such  errors  usually  are  obvious,  as  will  be  pointed  out 
in  connection  with  the  texts  in  which  they  are  found  (see  Chapters 
V  and  VI). 

If  both  of  the  above  alternatives  are  found  not  to  apply,  that  is, 
if  both  our  calculations  and  the  original  texts  are  free  from  error, 
we  are  obliged  to  accept  the  third  alternative  as  the  source  of 
trouble,  namely,  that  the  case  in  point  lies  without  the  operation  of 
our  rules.  In  such  cases  it  is  obviously  impossible  to  go  further  in 
the  present  state  of  our  knowledge.  Special  conditions  presented  by 
glyphs  whose  meanings  are  unknown  may  govern  such  cases.  At 
all  events,  the  failure  of  the  rules  under  1-4  to  reach  the  terminal 
dates  recorded  as  under  5  introduces  a  new  phase  of  glyph  study — 
the  meaning  of  unknown  forms  with  which  the  beginner  has  no  con- 
cern. Consequently,  when  a  text  falls  without  the  operation  of  the 
rules  given  in  this  chapter — a  very  rare  contingency — the  beginner 
should  turn  his  attention  elsewhere. 


Chapter  V 


THE  INSCRIPTIONS 

The  present  chapter  will  be  devoted  to  the  interpretation  of  texts 
drawn  from  monuments,  a  process  which  consists  briefly  in  the  appli- 
cation to  the  inscriptions  ^  of  the  material  presented  in  Chapters  III 
and  IV. 

Before  proceeding  with  this  discussion  it  will  first  be  necessary  to 
explain  the  method  followed  in  designating  particular  glyphs  in  a 


A 

B 

C 

D 

E 

F 

G 

H 

1  J 

K 

L 

M 

N 

1 

2 

3 

<x 

4 

y 

5 

6 

7 

8 

9 

10 

8 

Fig.  66,   Diagram  showing  the  method  of  designating  particular  glyphs  in  a  text. 


text.  We  have  seen  (p.  23)  that  the  Maya  glyphs  were  presented  in 
parallel  columns,  which  are  to  be  read  two  columns  at  a  time,  the 
order  of  the  individual  glyph-blocks  ^  in  each  pair  of  columns  being 
from  left  to  right  and  from  top  to  bottom.  For  convenience  in  refer- 
ring to  particular  glyphs  in  the  texts,  the  vertical  columns  of  glyph- 
blocks  are  lettered  from  left  to  right,  thus.  A,  B,  C,  D,  etc.,  and  the 
horizontal  rows  numbered  from  top  to  bottom,  thus,  1,  2,  3,  4,  etc. 
For  example,  in  figure  66  the  glyph-blocks  in  columns  A  and  B  are 
read  together  from  left  to  right  and  top  to  bottom,  thus,  Al  Bl,  A2 
B2,  A3  B3,  etc.    When  glyph-block  BlO  is  reached  the  next  in  order 

1  As  used  throughout  this  work,  the  word  "inscriptions"  is  applied  only  to  texts  from  the  monuments. 

2  The  term  glyph-block  has  been  used  instead  of  glyph  in  this  connection  because  in  many  inscriptions 
several  different  glyphs  are  included  in  one  glyph-block.  In  such  cases,  however,  the  glyphs  within  the 
glyph-block  follow  precisely  the  same  order  as  the  glyph-bl^  ^ks  themselves  follow  in  the  pairs  of  columns, 
that  is,  from  left  to  right  and  top  to  bottom. 

156 


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BULLETIN  57    PLATE  6 


B.    STELA  22,  NARANJO  D.    STELA  24,  NARANJO 


GLYPHS   REPRESENTING   INITIAL  SERIES,   SHOWING   USE  OF  BAR 
AND  DOT  NUMERALS  AND  NORMAL-FORM   PERIOD  GLYPHS 


MORLBY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


157 


is  Cl,  which  is  followed  by  Dl,  C2  D2,  C3  D3,  etc.  Again,  when  DlO 
is  reached  the  next  in  order  is  El,  which  is  followed  by  Fl,  E2  F2, 
E3  F3,  etc.  In  this  way  the  order  of  reading  proceeds  from  left  to 
right  and  from  top  to  bottom,  in  pairs  of  columns,  that  is,  G  H,  I  J, 
K  L,  and  M  jST  throughout  the  inscription,  and  usually  closes  with 
the  glyph-block  in  the  lower  right-hand  corner,  as  NlO  in  figure  66. 
By  this  simple  system  of  coordinates  any  particular  glyph  in  a  text 
may  be  readily  referred  to  when  the  need  arises.  Thus,  for  example, 
in  figure  66  gl3rph  a  is  referred  to  as  D3;  glyph  /?  as  F6;  glyph  j  as 
K4;  glyph  b  as  NlO.  In  a  few  texts  the  glyph-blocks  are  so  irregu- 
larly placed  that  it  is  impracticable  to  designate  them  by  the  above 
coordinates.  In  such  cases  the  order  of  the  glyph-blocks  will  be 
indicated  by  numerals,  1, 2,  3,  etc.  In  two  Copan  texts.  Altar  S  (fig. 
81)  and  Stela  J  (pi.  15),  made  from  the  drawings  of  Mr.  Maudslay, 
his  numeration  of  the  glyphs  has  been  followed.  This  numeration 
appears  in  these  two  figures. 

Texts  Recording  Initial  Series 

Because  of  the  fundamental  importance  of  Initial  Series  in  the 
Maya  system  of  chronology,  the  first  class  of  texts  represented  will 
illustrate  this  method  of  dating.  Moreover,  since  the  normal  forms 
for  the  numerals  and  the  period  glyphs  will  be  more  easily  recognized 
by  the  beginner  than  the  corresponding  head  variants,  the  first  Initial 
Series  given  will  be  found  to  have  all  the  numerals  and  period  glyphs 
expressed  by  normal  forms. ^ 

In  plate  6  is  figured  the  drawing  of  the  Initial  Series  ^  from  Zoo- 
mo  rph  P  at  Quirigua,  a  monument  which  is  said  to  be  the  finest  piece  of 
aboriginal  sculpture  in  the  western  hemisphere.  Our  text  opens  with 
one  large  glyph,  which  occupies  the  space  of  four  glyph-blocks,  Al- 
B2.^  Analysis  of  this  form  shows  that  it  possesses  all  the  elements 
mentioned  on  page  65  as  belonging  to  the  so-called  Initial-series 
introducing  glyph,  without  which  Initial  Series  never  seem  to  have 
been  recorded  in  the  inscriptions.    These  elements  are:  (1)  the  trinal 

1  Initial  Series  which  have  all  their  period  glyphs  expressed  by  normal  forms  are  comparatively  rare; 
consequently  the  four  examples  presented  in  pi.  6,  although  they  are  the  best  of  their  kind,  leave  some- 
thing to  be  desired  in  other  ways.  In  pi.  6,  A,  for  example,  the  month  sign  was  partially  effaced  though 
it  is  restored  in  the  accompanying  reproduction ;  in  5  of  the  same  plate  the  closing  glyph  of  the  Supple- 
mentary Series  (the  month-sign  indicator)  is  wanting,  although  the  month  sign  itself  is  very  clear. 
Again,  in  B  the  details  of  the  day  glyph  and  month  glyph  are  partially  effaced  (restored  in  the  repro- 
duction), and  in  C,  although  the  entire  text  is  very  clear,  the  month  sign  of  the  terminal  date  irregularly 
follows  immediately  the  day  sign.  However,  in  spite  of  these  slight  irregularities,  it  has  seemed  best  to 
present  these  particular  texts  as  the  first  examples  of  Initial  Series,  because  their  period  glyphs  are 
expressed  by  normal  forms  exclusively,  which,  as  pointed  out  above,  are  more  easily  recognized  on  account 
of  their  greater  differentiation  than  the  corresponding  head  variants. 

2  In  most  of  the  examples  presented  in  this  chapter  the  full  inscription  is  not  shown,  only  that  part  of 
the  text  illustrating  the  particular  point  in  question  being  given.  For  this  reason  reference  will  be 
made  in  each  case  to  the  publication  in  which  the  entire  inscription  has  been  reproduced.  The  full 
text  on  Zoomorph  P  at  Quirigua  will  be  found  in  Maudslay,  1889-1902:  u,  pis.  53,  54,  55,  56,  57,  59,  63,  64. 

3  All  glyphs  expressed  in  this  way  are  to  be  understood  as  inclusive.  Thus  A1-B2  signifies  4  glyphs, 
namely,  Al,  Bl,  A2,  B2, 


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[BULL.  57 


superfix,  (2)  the  pair  of  comblike  lateral  appendages,  (3)  the  normal 
form  of  the  tun  sign,  (4)  the  trinal  subfix,  and  (5)  the  variable  central 
element.  As  stated  above,  all  these  appear  in  the  large  glyph  Al- 
B2.  Moreover,  a  comparison  of  A1-B2  with  the  introducing  gl3rphs 
given  in  figure  24  shows  that  these  forms  are  variants  of  one  and 
the  same  sign.  Consequently,  in  A1-B2  we  have  recorded  an  Initial- 
series  introducing  glyph.  The  use  of  this  sign  is  so  highly  specialized 
that,  on  the  basis  of  its  occurrence  alone  in  a  text,  the  student  is 
perfectly  justified  in  assuming  that  an  Initial  Series  will  immediately 
follow.^  Exceptions  to  this  rule  are  so  very  rare  (see  p.  67)  that  the 
beginner  will  do  well  to  disregard  them  altogether. 

The  next  glyph  after  the  introducing  glyph  in  an  Initial  Series  is  the 
cycle  sign,  the  highest  period  ever  foimd  in  this  kind  of  coimt^.  The 
cycle  sign  in  the  present  example  appears  in  A3  with  the  coefficient 
9  (1  bar  and  4  dots).  Although  the  period  glyph  is  partially  effaced 
in  the  original  enough  remains  to  trace  its  resemblance  to  the  normal 
form  of  the  cycle  sign  shown  in  figiu-e  25,  a-c.  The  outline  of  the  repeated 
Cauac  sign  appears  in  both  places.  We  have  then,  in  this  glyph,  the 
record  of  9  cycles^.  The  glyph  following  the  cycle  sign  in  an  Initial 
Series  is  always  the  katun  sign,  and  this  should  appear  in  B3,  the  glyph 
next  in  order.  This  glyph  is  quite  clearly  the  normal  form  of  the  katun 
sign,  as  a  comparison  of  it  with  figure  27,  a,  h,  the  normal  form  for 
the  katun,  will  show.  It  has  the  normal-form  numeral  18  (3  bars 
and  3  dots)  prefixed  to  it,  and  this  whole  glyph  therefore  signifies 
18  katuns.  The  next  glyph  should  record  the  tuns,  and  a  comparison 
of  the  glyph  in  A4  with  the  normal  form  of  the  tun  sign  in  figure  29, 
a,  h,  shows  this  to  be  the  case.  The  numeral  5  (1  bar  prefixed  to  the 
tun  sign)  shows  that  this  period  is  to  be  used  5  times;  that  is,  multi- 
plied by  5.  The  next  glyph  (B4)  should  be  the  uinal  sign,  and  a 
comparison  of  B4  with  figure  31,  a-c,  the  normal  form  of  the  uinal  sign, 
shows  the  identity  of  these  two  glyphs.  The  coefficient  of  the  uinal 
sign  contains  as  its  most  conspicuous  element  the  clasped  hand, 
which  suggests  that  we  may  have  0  uinals  recorded  in  B4.  A  com- 
parison of  this  coefficient  with  the  sign  for  zero  in  figure  54  proves 
this  to  be  the  case.  The  next  glyph  (A5)  should  be  the  kin  sign,  the 
lowest  period  involved  in  recording  Initial  Series.  A  comparison  of 
A5  with  the  normal  form  of  the  kin  sign  in  figure  34,  a,  shows  that  these 
two  forms  are  identical.  The  coefficient  of  A5  is,  moreover,  exactly 
like  the  coefficient  of  B4,  which,  we  have  seen,  meant  zero,  hence 
glyph  A5  stands  for  0  kins.  Summarizing  the  above,  we  may  say 
that  glyphs  A3-A5  record  an  Initial-series  number  consisting  of  6 
cycles,  18  katuns,  5  tuns,  0  uinals,  and  0  kins,  which  we  may  write 
thus:   9.18.5.0.0  (see  p.  138,  footnote  1). 

1  The  introducing  glyph,  so  far  as  the  writer  knows,  always  standjuat  the  beginning  of  an  inscription, 
or  in  the  second  glyph-block,  that  is,  at  the  top.  Hence  an  Initial  ^^^^k^  can  never  precede  it. 

2  The  Initial  Series  on  Stela  10  at  Tikal  is  the  only  exception  kno\\^:   See  pp.  123-127. 

?  As  will  appear  in  the  following  examples,  nearly  all  Initial  Series  have  9  as  their  cycle  coefficient. 


MORLHY]      IK^TRODUCTIOIT  TO  STUDY  OF  MAYA  HIEROGLYPHS  159 


Now  let  US  turn  to  Chapter  IV  and  apply  the  several  steps  there 
given,  by  means  of  which  Maya  numbers  may  be  solved.  The  first 
step  on  page  134  was  to  reduce  the  given  number,  in  this  case 
9.18.5.0.0,  to  imits  of  the  first  order;  this  may  be  done  by  multiplying 
the  recorded  coefficients  by  the  numerical  values  of  the  periods  to 
which  they  are  respectively  attached.  These  values  are  given  in 
Table  XIII,  and  the  sum  of  the  products  arising  from  their  multi- 
jilication  by  the  coefficients  recorded  in  the  Initial  Series  in  plate  6,  A 
are  given  below: 

A3=  9X144,000  =  1,296,000 
B3  =  18X  7,200=  129,600 
A4=  5X  360=  1,800 
B4  =  0  X  20  =  0 
A5=  OX  1=  0 


1,427,  400 

Therefore  1,427,400  will  be  the  namber  used  in  the  following  calcu- 
lations. 

The  second  step  (see  step  2,  p.  135)  is  to  determine  the  starting 
point  from  which  this  number  is  counted.  According  to  rule  2,  page 
136,  if  the  number  is  an  Initial  Series  the  starting  point,  although 
never  recorded,  is  practically  always  the  date  4  Ahau  8  Cumhu. 
Exceptions  to  this  rule  are  so  very  rare  that  they  may  be  disregarded 
by  the  beginner,  and  it  may  be  taken  for  granted,  therefore,  in  the 
present  case,  that  our  number  1,427,400  is  to  be  counted  from  the 
date  4  Ahau  8  Cumhu. 

The  third  step  (see  step  3,  p.  136)  is  to  determine  the  direction  of 
the  count,  whether  forward  or  backward.  In  this  connection  it  was 
stated  that  the  general  practice  is  to  count  forward,  and  that  the 
studeQt  should  always  proceed  upon  this  assumption.  However, 
in  the  present  case  there  is  no  room  for  uncertainty,  since  the  direc- 
tion of  the  count  in  an  Initial  Series  is  governed  by  an  invariable 
rule.  In  Initial  Series,  according  to  the  rule  on  page  137,  the  count 
is  always  forward,  consequently  1,427,400  is  to  be  counted  forward 
from  4  Ahau  8  Cumliu. 

The  fourth  step  (see  step  4,  p.  138)  is  to  count  the  given  number 
from  its  starting  point;  and  the  rules  governing  this  process  will  be 
found  on  pages  139-143.  Since  our  given  number  (1,427,400)  is 
greater  than  18,980,  or  1  Calendar  Round,  the  preliminary  rule  on 
page  143  applies  in  the  present  case,  and  we  may  therefore  sub- 
tract from  1,427,400  all  the  Calendar  Rounds  possible  before  proceed- 
ing to  count  it  from  the  starting  point.  By  referring  to  Table 
XVI,  it  appears  that  1,427,400  contains  75  complete  Calendar 
Rounds,  or  1,423,500;  ^nce,  the  ktter  number  may  be  subtracted 


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[BULL.  57 


from  1,427,400  without  affecting  the  value  of  the  resulting  terminal 
date:  1,427,400-1,423,500  =  3,900.  In  other  words,  in  counting 
forward  3,900  from  4  Ahau  8  Cumhu,  the  same  terminal  date  will 
be  reached  as  though  we  had  counted  forward  1,427,400.^ 

In  order  to  find  the  coefficient  of  the  day  of  the  terminal  date,  it 
is  necessary,  by  rule  1,  page  139,  to  divide  the  given  number  or  its 
equivalent  by  13;  3,900^13  =  300.  Now  since  there  is  no  fractional 
part  in  the  resulting  quotient,  the  numerator  of  an  assumed  fractional 
part  will  be  0;  counting  forward  0  from  the  coefficient  of  the  day 
of  the  starting  point,  4  (that  is,  4  Ahau  8  Cumliu),  we  reach  4  as  the 
coefficient  of  the  day  of  the  terminal  date. 

In  order  to  find  the  day  sign  of  the  terminal  date,  it  is  necessary, 
under  rule  2,  page  140,  to  divide  the  given  number  or  its  equivalent  by 
20;  3,900  ^  20  =  195.  Since  there  is  no  fractional  part  in  the  resulting 
quotient,  the  numerator  of  an  assumed  fractional  part  will  be  0; 
coimting  forward  0  in  Table  I,  from  Ahau,  the  day  sign  of  the  start- 
ing point  (4  Ahau  8  Cumhu),  we  reach  Ahau  as  the  day  sign  of  the 
terminal  date.  In  other  words,  in  counting  forward  either  3,900  or 
1,427,400  from  4  Ahau  8  Cumhu,  the  day  reached  will  be  4  Ahau. 
It  remains  to  show  what  position  in  the  year  this  day  4  Ahau  distant 
1,427,400  from  the  date  4  Ahau  8  Cumhu,  occupi3d. 

In  order  to  find  the  position  in  the  year  which  the  day  of  the  ter- 
minal date  occupied,  it  is  necessary,  under  rule  3,  page  141,  to  divide 
the  given  number  or  its  equivalent  by  365;  3,900 365  =  10f|f. 
Since  the  numerator  of  the  fractional  part  of  the  residting  quotient  is 
250,  to  reach  the  year  position  of  the  day  of  the  terminal  date  desired 
it  is  necessary  to  count  250  forward  from  8  Cumhu,  the  year  position 
of  the  day  of  the  starting  point  4  Ahau  8  Cumhu.  It  appears  from 
Table  XV,  in  which  the  365  positions  of  the  year  are  given,  that  after 
position  8  Cumhu  there  are  only  16  positions  in  the  year — 11  more 
in  Cumhu  and  5  in  TJayeb.  These  must  be  subtracted,  therefore,  from 
250  in  order  to  bring  the  count  to  the  end  of  the  year;  250  —  16  =  234, 
so  234  is  the  number  of  positions  we  must  count  forward  in  the  new 
year.  It  is  clear  that  the  first  1 1  uinals  in  the  year  will  use  up  exactly 
220  of  our  234  positions  (11  x20  =  220),  and  that  14  positions  will 
be  left,  which  must  be  counted  in  the  next  uinal,  the  12th.  But  the 
12th  uinal  of  the  year  is  Ceh  (see  Table  XV) ;  counting  forward  14 
positions  in  Ceh,  we  reach  13  Ceh,  which  is,  therefore,  the  month 
glyph  of  our  terminal  date.  In  other  words,  coimting  250  forward 
from  8  Cumhu,  position  13  Ceh  is  reached.  Assembling  the  above 
values,  we  find  that  by  calculation  we  have  determined  the  terminal 
date  of  the  Initial  Series  in  plate  6,  ^,  to  be  4  Ahau  IS  Ceh. 


1  In  the  present  case  therefore  so  far  as  these  calculations  are  concerned,  3,900  is  the  equivalent  of 
1,427,400. 


MORLBY]      IN^TKODUCTIOE'  TO  STUDY  OF  MAYA  HIEKOGLYPHS 


161 


At  this  point  there  are  several  checks  which  the  student  may  apply 
to  his  result  in  order  to  test  the  accuracy  of  his  calculations;  for 
instance,  in  the  present  example  if  115,  the  diflerence  between  365 
and  250  (115  +  250  -=365)  is  counted  forward  from  position  13  Ceh,  po- 
sition 8  Cumhu  will  be  reached  if  our  calculations  were  correct.  This 
is  true  because  there  are  only  365  positions  in  the  year,  and  having 
reached  13  Ceh  in  counting  forward  250  from  8  Cumliu,  counting  the 
remaining  115  days  forward  from  day  reached  by  250,  that  is,  13  Ceh, 
we  should  reach  our  starting  point-  (8  Cumhu)  again.  Another  good 
check  in  the  present  case  would  be  to  count  backward  250  from 
13  Ceh;  if  our  calculations  have  been  correct,  the  starting  point 
8  Cumhu  will  be  reached.  Still  another  check,  which  may  be  applied 
is  the  following:  From  Table  VII  it  is  clear  that  the  day  sign  Ahau 
can  occupy  only  positions  3,  8,  13,  or  18  in  the  divisions  of  the  year;^ 
hence,  if  in  the  above  case  the  coefficient  of  Ceh  had  been  any  other 
number  but  one  of  these  four,  our  calculations  would  have  been 
incorrect. 

We  come  now  to  the  final  step  (see  step  5,  p.  151),  the  actual  finding 
of  the  glyphs  in  our  text  which  represent  the  two  parts  of  the  ter- 
minal date — the  day  and  its  corresponding  position  in  the  year.  If 
we  have  made  no  arithmetical  errors  in  calculations  and  if  the  text 
itself  presents  no  irregular  and  unusual  features,  the  terminal  date 
recorded  should  agree  with  the  terminal  date  obtained  by  calculation. 

It  was  explained  on  page  152  that  the  two  parts  of  an  Initial- 
series  terminal  date  are  usually  separated  from  each  other  by  several 
intervening  glyphs,  and  further  that,  although  the  day  part  follows 
immediately  the  last  period  glyph  of  the  number  (the  kin  glyph), 
the  month  part  is  not  recorded  until  after  the  close  of  the  Supplemen- 
tary Series,  usually  a  matter  of  six  or  seven  glyphs.  Returning  to 
our  text  (pi.  6,  A),  we  find  that  the  kins  are  recorded  in  A5,  therefore 
the  day  part  of  the  terminal  date  should  appear  in  B5.  The  glyph 
in  B5  quite  clearly  records  the  day  4  Ahau  by  means  of  4  dots  prefixed 
to  the  sign  shown  in  figure  16,  e^-g^,  which  is  the  form  for  the  day 
name  Ahau,  thereby  agreeing  with  the  value  of  the  day  part  of  the 
terminal  date  as  determined  by  calculation.  So  far  then  we  have  read 
our  text  correctly.  Following  along  the  next  six  or  seven  glyphs, 
A6-Cla,  which  record  the  Supplementary  Series,  ^  we  reach  in  Cla 
a  sign  similar  to  the  forms  shown  in  figure  65.  This  glyph,  which 
always  has  a  coefficient  of  9  or  10,  was  designated  on  page  152  the 
month-sign  ^^ndicator,"  since  it  usually  immediately  precedes  the 
month  sign  in  Initial-series  terminal  dates.  In  Cla  it  has  the  coeffi- 
cient 9  (4  dots  and  1  bar)  and  is  followed  in  Clb  by  the  month  part 

^1  It  should  be  remembered  in  this  comiection,  as  explained  on  pp.  47, 55,  that  the  positions  in  the  divi- 
sions of  the  year  which  the  Maya  caUed  3,  8,  13,  and  18  correspond  in  our  method  of  naming  the  positions 
of  the  days  in  the  months  to  the  4th,  9th,  14th,  and  19th  positions,  respectively. 

2As  stated  in  footnote  1,  p.  152,  the  meaning  of  the  Supplementary  Series  has  not  yet  been  worked  out. 

43508°— Bull,  57—15  11 


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of  the  terminal  date,  13  Ceh.  The  bar  and  dot  numeral  13  appears 
very  clearly  above  the  month  sign,  which,  though  partially  effaced, 
yet  bears  sufficient  resemblance  to  the  sign  for  Cell  in  figure  19, 
u,  V,  to  enable  us  to  identify  it  as  such. 

Our  complete  Initial  Series,  therefore,  reads:  9.18.5.0.0  4  Ahau  13 
Ceh,  and  since  the  terminal  date  recorded  in  B5,  Clb  agrees  with  the 
terminal  date  determined  by  calculation,  we  may  conclude  that  this 
text  is  without  error  and,  furthermore,  that  it  records  a  date,  4  Ahau 
13  Ceh,  which  was  distant  9.18.5.0.0  from  the  starting  point  of  Maya 
chronology.  The  writer  interprets  this  text  as  signifying  that 
9.18,5.0.0  4  Ahau  13  Ceh  was  the  date  on  which  Zoomorph  P  at  Qui- 
rigua  was  formally  consecrated  or  dedicated  as  a  time-marker,  or  in 
other  words,  that  Zoomorph  P  was  the  monument  set  up  to  mark  the 
hotun,  or  5-tun  period,  which  came  to  a  close  on  the  date  9.18.5.0.0  4 
Ahau  13  Ceh  of  Maya  chronology.  ^ 

In  plate  6,  B,  is  figured  a  drawing  of  the  Initial  Series  on  Stela  22  at 
Naranjo.^  The  text  opens  in  Al  with  the  Initial-series  introducing 
glyph,  which  is  followed  in  B1-B3  by  the  Initial-series  number 
9.12.15.13.7.  The  five  period  glyphs  are  all  expressed  by  their  cor- 
responding normal  forms,  and  the  student  will  have  no  difficulty  in 
identifying  them  and  reading  the  number,  as  above  recorded. 

By  means  of  Table  XIII  this  number  may  be  reduced  to  units  of 
the  1st  order,  in  which  form  it  may  be  more  conveniently  used.  This 
reduction,  which  forms  the  first  step  in  the  process  of  solving  Maya 
numbers  (see  step  1,  p.  134),  follows: 

Bl=  9X144,000  =  1,296,000 

A2  =  12X     7,200=  86,400 

B2  =  15X        360=  5,400 

A3  =  13x         20=  260 

B3=  7X  1=  7 

1,  388,  067 

And  1,388,067  will  be  the  number  used  in  the  following  calculations. 

The  next  step  is  to  find  the  starting  point  from  which  1,388,067  is 
counted  (see  step  2,  p.  135).  Since  this  number  is  an  Initial  Series,  in 
all  probability  its  starting  point  will  be  the  date  4  Ahau  8  Cumhu ;  at 
least  it  is  perfectly  safe  to  proceed  on  that  assumption. 

The  next  step  is  to  find  the  direction  of  the  count  (see  step  3,  p.  136) ; 
since  our  number  is  an  Initial  Series,  the  count  can  only  be  forward 
(see  rule  2,  p.  137).' 

1  The  reasons  which  have  led  the  writer  to  this  conclusion  are  given  at  some  length  on  pp.  33-36. 

2  For  the  full  text  of  this  inscription  see  Maler,  1908  b:  pi.  36. 

3  Since  nothing  but  Initial-series  texts  will  be  presented  in  the  plates  and  figures  immediately  following, 
a  fact  which  the  student  will  readily  detect  by  the  presence  of  the  introducing  glyph  at  the  head  of  each 
text,  it  is  unnecessary  to  repeat  for  each  new  text  step  2  (p.  135)  and  step  3  (p.  136),  which  explain  how  to 
determine  the  starting  point  of  the  count  and  the  direction  of  the  count,  respectively;  and  the  student 
may  assume  that  the  starting  point  of  the  several  Initial  Series  hereinafter  figured  will  always  be  the  date 
4  Ahau  8  Cumhu  and  that  the  direction  of  the  count  will  always  be  forward. 


MORLBY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  163 

Having  aetermined  the  number  to  be  counted,  the  starting  point 
from  which  the  count  commences,  and  the  direction  of  the  count,  we 
may  now  proceed  with  the  actual  process  of  counting  (see  step  4, 
p.  138). 

Since  1,388,067  is  greater  than  18,980  (1  Calendar  Round),  we  may 
deduct  from  the  former  number  all  the  Calendar  Rounds  possible  (see 
preliminary  rule,  page  143).  According  to  Table  XVI  it  appears 
that  1,388,067  contains  73  Calendar  Rounds,  or  1,385,540;  after  de- 
ducting this  from  the  given  number  we  have  left  2,527  (1,388,067  — 
1,385,540),  a  far  more  convenient  number  to  handle  than  1,388,067. 

Applying  rule  1  (p.  139)  to  2,527,  we  have:  2,527-^13  =  1943^, 
and  counting  forward  5,  the  numerator  of  the  fractional  part  of  the 
quotient,  from  4,  the  day  coefficient  of  the  starting  point,  4  Ahau  8 
Cumliu,  we  reach  9  as  the  day  coefficient  of  the  terminal  date. 

Applying  rule  2  (p.  140)  to  2,527,  we  have:  2,527 -^20  =  126 2V; 
and  counting  forward  7,  the  numerator  of  the  fractional  part  of  the 
quotient,  from  Ahau,  the  day  sign  of  our  starting  point,  4  Ahau  8 
Cumhu,  in  Table  I,  we  reach  Manik  as  the  day  sign  of  the  terminal 
date.    Therefore,  the  day  of  the  terminal  date  will  be  9  Manik. 

Applying  rule  3  (p.  141)  to  2,527,  we  have:  2,527 365  =  6f||; 
and  counting  forward  337,  the  numerator  of  the  fractional  part  of 
the  quotient,  from  8  Cumhu,  the  year  position  of  the  starting  point, 
4  Ahau  8  Cumhu,  in  Table  XV,  we  reach  0  Kayab  as  the  year  position 
of  the  terminal  date.  The  calculations  by  means  of  v/hich  0  Kayab  is 
reached  are  as  follows:  After  8  Cumhu  there  are  16  positions  in  the 
year,  which  we  must  subtract  from  337;  337  —  16  =  321,  which  is  to 
be  counted 'forward  in  the  new  year.  This  number  contains  just  1 
more  than  16  uinals,  that  is,  321  =  (16  X20)  + 1;  hence  it  will  reach 
through  the  first  16  uinals  in  Table  XV  and  to  the  first  position  in 
the  17th  uinal,  0  Kayab.  Combining  this  with  the  day  obtained 
above,  we  have  for  our  terminal  date  determined  by  calculation,  9 
Manik  0  Kayab. 

The  next  and  last  step  (see  step  5,  p.  151)  is  to  find  the  above  date 
in  the  text.  In  Initial  Series  (see  p.  152)  the  two  parts  of  the  ter- 
minal date  are  generally  separated,  the  day  part  usually  following 
immediately  the  last  period  glyph  and  the  month  part  the  closing 
glyph  of  the  Supplementary  Series.  In  plate  6,  B,  the  last  period  glyph, 
as  we  have  seen,  is  recorded  in  B3;  therefore  the  day  should  appear 
in  A4.  Comparing  the  glyph  in  A4  with  the  sign  for  Manik  in  figure 
16,  y,  the  two  forms  are  seen  to  be  identical.  Moreover,  A4  has  the 
bar  and  dot  coefficient  9  attached  to  it,  that  is,  4  dots  and  1  bar;  con- 
sequently  it  is  clear  that  in  A4  we  have  recorded  the  day  9  Manik, 
the  same  day  as  reached  by  calculation.  For  some  unknown  reason, 
at  Naranjo  the  month  glyphs  of  the  Initial-series  terminal  dates  do 
not  regularly  follow  the  closing  glyphs  of  the  Supplementary  Series; 


164 


BUREAU  OF  AMEEICAN  ETHNOLOGY 


[BULL.  57 


indeed,  in  the  text  here  under  discussion,  so  far  as  we  can  judge  from 
the  badly  effaced  glyphs,  no  Supplementary  Series  seems  to  have 
been  recorded.  However,  reversing  our  operation,  we  know  by 
calculation  that  the  month  part  should  be  0  Kayab,  and  by  referring 
to  figure  49  we  find  the  only  form  which  can  be  used  to  express  the 
0  position  with  the  month  signs — the  so-called  ^^spectacles''  glyph — 
which  must  be  recorded  somewhere  in  this  text  to  express  the  idea 
0  with  the  month  sign  Kayab.  Further,  by  referring  to  figure  19, 
d'-f,  we  may  fix  in  our  minds  the  sign  for  the  month  Kayab,  which 
should  also  appear  in  the  text  with  one  of  the  forms  shown  in  figure  49. 

Returning  to  our  text  once  more  and  following  along  the  glyphs 
after  the  day  in  A4,  we  pass  over  B4,  A5,  and  B5  without  finding  a 
glyph  resembling  one  of  the  forms  in  figure  49  joined  to  figure  19, 
d'-f;  that  is,  0  Kayab.  However,  in  A6  such  a  glyph  is  reached, 
and  the  student  will  have  no  difficulty  in  identifying  the  month  sign 
with  d'-f  in  the  above  figure.  Consequently,  we  have  recorded  in 
A4,  A6  the  same  terminal  date,  9  Manik  0  Kayab,  as  determined  by 
calculation,  and  may  conclude,  therefore,  that  our  text  records  without 
error  the  date  9.12.15.13.7  9  Manik  0  Kayab ^  of  Maya  chronology. 

The  next  text  presented  (pi.  6,  C)  shows  the  Initial  Series  from 
Stela  I  at  Quirigua.^  Again,  as  in  plate  6,  A,  the  introducing  glyph 
occupies  the  space  of  four  glyph-blocks,  namely,  A1-B2.  Immedi- 
ately after  this,  in  A3-A4,  is  recorded  the  Initial-series  number 
9.18.10.0.0,  all  the  period  glyphs  and  coefficients  of  which  are 
expressed  by  normal  forms.  The  student's  attention  is  called  to  the 
form  for  0  used  with  the  uinal  and  kin  signs  in  A4a  and  A4b,  respec- 
tively, which  differs  from  the  form  for  0  recorded  with  the  uinal  and 
kin  signs  in  plate  6,  A,  B4,  and  A5,  respectively.  In  the  latter  text 
the  0  uinals  and  0  kins  were  expressed  by  the  hand-  and  curl  form  for 
zero  shown  in  figure  54;  in  the  present  text,  however,  the  0  uinals 
and  0  kins  are  expressed  by  the  form  for  0  shown  in  figure  47,  a  new 
feature. 

Reducing  the  above  number  to  units  of  the  1st  order  by  means  of 
Table  XIII,  we  have: 

A3=  9X144,000  =  1,296,000 
B3a  =  18x  7,200=  129,600 
B3b  =  10x  360=  3,600 
A4a=  OX  20=  0 
A4b=  OX  1=  0 

1,  429,  200 

1  As  will  appear  later,  in  connection  with  the  discussion  of  the  Secondary  Series,  the  Initial-series  date 
of  a  monument  does  not  always  correspond  with  the  ending  date  of  the  period  whose  close  the  monument 
marks.  In  other  words,  the  Initial-series  date  is  not  always  the  date  contemporaneous  with  the  formal 
dedication  of  the  monument  as  a  time-marker.  This  point  will  appear  much  more  clearly  when  the  function 
of  Secondary  Series  has  been  explained. 

2  For  the  full  text  of  this  inscription  see  Hewett,  1911:  pi.  xxxv  C. 


MORLBT]      INTEODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  165 

Deducting  from  this  number  all  the  Calendar  Rounds  possible,  75 
(see  Table  XYI),  it  may  be  reduced  to  5,700  without  affecting  its 
value  in  the  present  connection. 

Applying  rules  1  and  2  (pp.  139  and  140,  respectively)  to  this  num- 
ber, the  day  reached  will  be  found  to  be  10  Ahau ;  and  by  applying 
rule  3  (p.  141),  the  position  of  this  day  in  the  year  will  be  found  to  be 
8  Zac»  Therefore,  by  calculation  we  have  determined  that  the  ter- 
minal date  reached  by  this  Initial  Series  is  10  Ahau  8  Zac.  It  remains 
to  find  this  date  in  the  text.  The  regular  position  for  the  day  in 
Initial-series  terminal  dates  is  immediately  following  the  last  period 
glyph,  which,  as  we  have  seen  above,  was  in  A4b.  Therefore  the  day 
glyph  should  be  B4a.  An  inspection  of  this  latter  glyph  will  show 
that  it  records  the  day  10  Aliau,  both  the  day  sign  and  the  coefficient 
being  unusually  clear,  and  practically  unmistakable.  Compare  B4a 
with  figure  16,  e'-g' ,  the  sign  for  the  day  name  Ahau.  Consequently 
the  day  recorded  agrees  with  the  day  determined  by  calculation.  The 
month  glyph  in  this  text,  as  mentioned  on  page  157,  footnote  1,  occurs 
out  of  its  regular  position,  following  immediately  the  day  of  the 
terminal  date. 

As  mentioned  on  page  153,  when  the  month  glyph  in  Initial-series 
terminal  dates  is  not  to  be  found  in  its  usual  position,  it  will  be  found 
in  the  regular  position  for  the  month  glyphs  in  all  other  kinds  of 
dates  in  the  inscriptions,  namely,  immediately  following  the  day  glyph 
to  which  it  belongs.  In  the  present  text  we  found  that  the  day,  10 
Ahau,  was  recorded  in  B4a;  hence,  since  the  month  glyph  was  not 
recorded  in  its  regular  position,  it  must  be  in  B4b,  immediately  fol- 
lowing the'  day  glyph.  By  comparing  the  glyph  in  B4b  with  the 
month  signs  in  figure  19,  it  will  be  found  exactly  like  the  month  sign 
for  Zac  {s-t),  and  we  may  therefore  conclude  that  this  is  our  month 
glyph  and  that  it  is  Zac.  The  coefficient  of  B4b  is  quite  clearly  8  and 
the  month  part  therefore  reads,  8  Zac.  Combining  this  with  the  day 
recorded  in  B4a,  we  have  the  date  10  Ahau  8  Zac,  which  corresponds 
with  the  terminal  date  determined  by  calculation.  The  whole  text 
therefore  reads  9.18.10.0.0  10  Ahau  8  Zac. 

It  will  be  noted  that  this  date  9.18.10.0.0  10  Ahau  8  Zac  is  just 
5.0.0  (5  tuns)  later  than  the  date  recorded  by  the  Initial  Series  on 
Zoomorph  P  at  Quirigua  (see  pi.  6,  ^).  As  explained  in  Chapter  II 
(pp.  33-34),  the  interval  between  succeeding  monuments  at  Qui- 
rigua is  in  every  case  1,800  days,  or  5  tuns.  Therefore,  it  would  seem 
probable  that  at  Quirigua  at  least  this  period  was  the  unit  used  for 
marking  the  lapse  of  time.  As  each  5-tun  period  was  completed,  its 
close  was  marked  by  the  erection  of  a  monument,  on  which  was 
recorded  its  ending  date.  Thus  the  writer  believes  Zoomorph  P 
marked  the  close  of  the  5-tun  period  ending  9.18.5.0.0  4  Ahau  13  Geh, 
and  Stela  I,  the  5-tun  period  next  following,  that  ending  9.18.10.0.0 


166 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


10  Ahau  8  Zac.  In  other  words,  Zoomorph  P  and  Stela  I  were  two 
successive  time-markers,  or  period  stones,"  in  the  chronological 
record  at  Quirigua.  For  this  5-tun  period  so  conspicuously  recorded 
in  the  inscriptions  from  the  older  Maya  cities  the  writer  would 
suggest  the  name  Tiotun,  7io  meaning  5  in  Maya  and  tun  being  the 
name  of  the  360-day  period.  This  word  has  an  etymological  parallel 
in  the  Maya  word  for  the  20-tun  period,  Tcatun,  which  we  have 
seen  may  have  been  named  directly  from  its  numerical  value,  leal 
being  the  word  for  20  in  Maya  and  Icaltun  contracted  to  katun, 
thus  meaning  20  tuns.  Although  no  glyph  for  the  Jiotun  has  as  yet 
been  identified,^  the  writer  is  inclined  to  believe  that  the  sign  in 
figure  67,  a,  h,  which  is  frequently  encountered  in  the  texts,  will  be 
found  to  represent  this  time  period.  The  bar  at  the  top  in  both 
a  and  h,  figure  67,  surely  signifies  5;  therefore  the  glyph  itself  must 
mean  "  1  tun."    This  form  recalls  the  very  unusual  variant  of  the  tim 


from  Palenque  (see  fig.  29,  7i). 
element. 


Both  have  the  wing  and  the  (*) 


Fig.  67.   Signs  representing  the  hotun, 
or  5-tun,  period. 


The  next  Initial  Series  presented  (see 
pi.  6,  D)  is  from  Stela  24  at  Naranjo.^ 
The  text  opens  with  the  introducing 
glyph,  which  is  in  the  same  relative  posi- 
tion as  the  introducing  glyph  in  the  other 
Naranjo  text  (pi.  6,  B)  at  Al.  Then 
follows  regularly  in  B1-B3  the  number 
9.12.10.5.12,  the  numbers  and  period 
glyphs  of  which  are  all  expressed  by  normal  forms.  By  this  time  the 
student  should  have  no  difficulty  in  recognizing  these  and  in  deter- 
mining the  number  as  given  above.  Reducing  this  according  to 
rule  1,  page  134,  the  following  result  should  be  obtained: 

Bl=  9X144,000  =  1,296,000 
A2  =  12X  7,200=  86,400 
B2  =  10X  360=  3,600 
A3=  5X         20=  100 

B3  =  12x  1=  12 

1,  386,  112 

Deducting^  from  this  number  all  the  Calendar  Rounds  possible,  73 
(see  preliminary  rule,  p.  143,  and  Table  XVI),  we  may  reduce  it  to 
572  without  affecting  its  value  in  so  far  as  the  present  calculations^ 
are  concerned  (1,386,112-1,385,540).    First  applying  rule  1,  page 

1  So  far  as  the  writer  knows,  the  existence  of  a  period  containing  5  tuns  has  not  been  suggested  heretofore,  ^ 
The  very  general  practice  of  closing  inscriptions  with  the  end  of  some  particular  5-tun,  period  ia  the  Long  « 
Count,  as  9.18.5.0.0,  or  9.18.10.0.0,  or  9.18.15.0.0,  or  9.19.0.0.0,  for  example,  seems  to  indicate  that  this  period 
was  the  unit  used  for  measuring  time  in  Maya  chronological  records,  at  least  in  the  southern  cities.  Conse- 
quently, it  seems  likely  that  there  was  a  special  glyph  to  express  this  unit. 

2  For  the  full  text  of  this  inscription  see  Maler,  1908  h:  pi.  39. 

3  The  student  should  note  that  from  this  point  steps  2  (p.  139)  and  3  (p.  140)  have  been  omitted  in  dis- 
cussing each  text  (see  p.  162,  footnote  3). 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57    PLATE  7 


A.    STELA  B,  COPAN 


QQQO^p  ooq 


poo 


i?.    STELA  A,  COPAN 


GLYPHS   REPRESENTING   INITIAL  SERIES,   SHOWING   USE  O^^^ 
AND   DOT   NUMERALS  AND   HEAD-VARIANT   PERIOD  GLYPHS 


MORLEY]      INTKODUCTION  TO  STUDY  OF  MAYA  HIEKOGLYPHS  167 


139,  and  next  rule  2,  page  140;  to  this  number  (572),  the  student  will 
find  the  day  reached  to  be  4  Eb.  And  applying  rule  3,  page  141,  he 
will  find  that  the  year  position  reached  will  be  10  Yax ;  ^  hence,  the 
terminal  date  as  determined  by  calculation  will  be  4  Eb  10  Yax. 

Turning  again  to  the  text  (pi.  6,  B),  the  next  step  (see  step  5,  p.  151) 
is  to  find  the  glyphs  representing  the  above  terminal  date.  In  this 
connection  it  should  be  remembered  that  the  day  part  of  an  Initial- 
series  terminal  date  usually  follows  immediately  the  last  period 
glyph  of  the  number.  The  glyph  in  A4,  therefore,  should  record  the 
day  reached.  Comparing  this  form  with  the  several  day  signs  in 
figure  16,  it  appears  that  A4  more  closely  resembles  the  sign  for  Eb 
(fig.  16,  s-u)  than  any  of  the  others,  hence  the  student  may  accept 
Eb  as  the  day  sign  recorded  in  A4.  The  4  dots  prefix:ed  to  this  sign 
show  that  the  day  4  Eb  is  here  indicated.  The  month  sign,  as  stated 
on  page  152,  usually  follows  the  last  glyph  of  the  Supplementary 
Series;  passing  over  B4,  A5,  B5,  and  A6,  we  reach  the  latter  glyph 
in  B6.  Compare  the  left  half  of  B6  with  the  forms  given  in  fi^wvQ 
65.  The  coefiicient  9  or  10  is  expressed  by  a  considerably  effaced 
head  numeral.  Immediately  following  the  month-sign  ''indicator" 
is  the  month  sign  itself  in'A7.  The  student  will  have  fit  tie  difficulty 
in  tracing  its  resemblance  to  the  month  Yax  in  figure  19,  g-,  r,  although 
in  A7  the  Yax  element  itself  appears  as  the  prefix  instead  of  as  the 
superfix,  as  in  €[  and  r,  just  cited.  This  difference,  however,  is  imma- 
terial. The  month  coefficient  is  quite  clearly  10,^  and  the  whole 
terminal  date  recorded  will  read  4  Eb  10  Yax,  which  corresponds 
exactly  with  the  terminal  date  determined  by  calculation.  We  may 
accept  this  text,  therefore,  as  recording  the  Initial-series  date 
9.12.10.5.12  4  Eb  10  Yax  of  Maya  chronology. 

In  the  foregoing  examples  nothmg  but  normal-form  period  glyphs 
have  been  presented,  in  order  that  the  first  exercises  in  deciphering  the 
inscriptions  may  be  as  easy  as  possible.  By  this  time,  however,  the 
student  should  be  sufficiently  famifiar  with  the  normal  forms  of  the 
period  glyphs  to  be  able  to  recognize  them  when  they  are  present  in 
the  text,  and  the  next  Initial  Series  figured  will  have  its  period  glyphs 
expressed  by  head  variants. 

In  A,  plate  7,  is  figured  the  Initial  Series  from  Stela  B  at  Copan.^ 
The  introducing  glyph  appears  at  the  head  of  the  inscription  in  Al 

1  In  each  of  the  above  cases— and,  indeed,  in  all  the  examples  following— the  student  should  perfom 
the  various  calculations  by  which  the  results  are  reached,  in  order  to  famiUarize  himself  with  the  work- 
ings of  the  Maya  chronological  system. 

2  The  student  may  apply  a  check  at  this  point  to  his  identification  of  the  day  sign  in  A4  as  being  that  for 
the  day  Eb.  Since  the  month  coefficient  in  A7  is  surely  10  (2  bars),  it  is  clear  from  Table  VII  that  the 
only  days  which  can  occupy  this  position  in  any  division  of  the  year  are  Ik,  Manik,  Eb,  and  Caban.  Now, 
by  comparing  the  sign  in  A4  with  the  signs  for  Ik,  Manik,  and  Caban,  c, and  a',  b',  respectively,  of  fig. 
16,  it  is  very  evident  that  A4  bears  no  resemblance  to  any  of  them;  hence,  since  Eb  is  the  only  one  left 
which  can  occupy  a  position  10,  the  day  sign  in  A4  must  be  Eb,  a  fact  supported  by  the  comparison  of 
A4  with  fig.  16,  s-u,  above. 

3  The  fuU  text  of  this  inscription  wiU  be  found  in  Maudslay,  1889-1901:  i,  pis.  35-37. 


168 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


and  is  followed  by  a  head-variant  glyph  in  A2,  to  which  is  prefixed  a 
bar  and  dot  coefficient  of  9.  By  its  position,  immediately  following 
the  introducing  glyph,  we  are  justified  in  assuming  that  A2  records 
9  cycles,  and  after  comparing  it  with  d-f,  figure  25,  where  the  head 
variant  of  the  cycle  sign  is  shown,  this  assumption  becomes  a  cer- 
tainty. Both  heads  have  the  same  clasped  hand  in  the  same  position, 
across  the  lower  part  of  the  face,  which,  as  explained  on  page  68,  is 
the  essential  element  of  the  cycle  head;  therefore,  A2  records  9 
cycles.  The  next  glyph,  A3,  should  be  the  katun  sign,  and  a  com- 
parison of  this  form  with  the  head  variant  for  katun  in  e-h,  figmre  27, 
shows  this  to  be  the  case.  The  determining  characteristic  (see  p. 
69)  is  probably  the  oval  in  the  top  of  the  head,  which  appears  in 
both  of  these  forms  for  the  katun.  The  katun  coefficient  is  15  (3 
bars).  The  next  glyph,  A4,  should  record  the  tuns,  and  by  comparing 
this  form  with  the  head  variant  for  the  tun  sign  in  e-g,  figure  29,  this 
also  is  found  to  be  the  case.  Both  heads  show  the  same  essential 
characteristic — the  fleshless  lower  jaw  (see  p.  70).  The  coefficient  is 
0  (compare  fig.  47).  The  uinal  head  in  A5  is  equally  unmistakable. 
Note  the  large  curl  protruding  from  the  back  part  of  the  mouth, 
which  was  said  (p.  71)  to  be  the  essential  element  of  this  sign. 
Compare  figure  31,  d-f,  where  the  head  variant  for  the  uinal  is  given. 
The  coefficient  of  A5  is  like  the  coefficient  of  A4  (0),  and  we  have 
recorded,  therefore,  0  uinals.  The  closing  period  glyph  of  the  Initial 
Series  in  A6  is  the  head  variant  for  the  kin  sign.  Compare  this  form 
with  figure  34,  e-g,  where  the  kin  head  is  figured.  The  determining 
characteristic  of  this  head  is  the  subfixial  element,  which  appears 
also  in  the  normal  form  for  the  kin  sign  (see  fig.  34,  a).  Again,  the 
coefficient  of  AG  is  like  the  coefficient  of  A4  and  A5,  hence  we  have 
recorded  here  0  kins. 

The  number  recorded  by  the  head-variant  period  glyphs  and 
normal-form  numerals  in  A2-A6  is  therefore  9.15.0.0.0;  reducing  this 
by  means  of  Table  XIII,  we  have : 


Deducting  from  this  number  all  the  Calendar  Rounds  possible,  73 
(see  Table  XYI),  it  may  be  reduced  to  18,460.  Appl3dng  to  this 
number  rules  1  and  2  (pp.  139  and  140,  respectively),  the  day  reached 
will  be  found  to  be  4  Ahau.  Applying  rule  3  (p.  141),  the  position  of 
4  Ahau  in  the  year  will  be  found  to  be  13  Yax.  Therefore  the  terminal 
date  determined  by  calculation  will  be  4  Ahau  13  Yax. 


A2=  9X144,000 
A3  =  15X  7,200 
A4=  Ox  360 
A5=  OX  20 
A6=  OX  1 


1,  296,  000 
108, 000 


0 
0 
0 


1,  404,  000 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  169 


According  to  step  5  (p.  151),  the  day  reached  should  follow  imme- 
diately the  last  period  g^P^^  ?  which  in  this  case  was  in  A6 ;  hence  the 
day  should  be  recorded  in  A7.  This  glyph  has  a  coefficient  4,  but 
the  glyph  does  not  resemble  either  of  the  forms  for  Aliau  shown  in 
B5,  plate  6,  A,  or  in  B4a,  C  of  the  same  plate.  However,  by  com- 
paring this  glyph  with  the  second  variant  for  the  day  sign  Ahau  in 
figure  16,  the  two  forms  will  be  found  to  be  identical,  and  we 

may  accept  A7  as  recording  the  day  4  Aliau.  Immediately  follow- 
ing in  A8  is  the  month  sign,  again  out  of  its  usual  place  as  in  plate 
6,  C.  Comparing  it  with  the  month  signs  in  figure  19,  it  will  be  found 
to  exactly  correspond  with  the  sign  for  Yax  in  q-r.  The  coefficient 
is  13.  Therefore  the  terminal  date  recorded,  4  Ahau  13  Yax,  agrees 
with  the  terminal  date  reached  by  calculation,  and  the  whole  Initial 
Series  reads  9.15.0.0.0  4  Aliau  13  Yax.  This  date  m_arks  the  close 
not  only  of  a  hotun  in  the  Long  Count,  but  of  a  katun  as  well. 

In  B,  plate  7,  is  figured  the  Initial  Series  from  Stela  A  at  Copan.^ 
The  introducing  glyph  appears  in  Al  Bl,  and  is  followed  by  the 
Initial-series  number  in  A2-A4.  The  student  will  have  no  difficulty 
in  picking  out  the  clasped  hand  in  A2,  the  oval  in  the  top  of  the  head 
in  B2,  the  fleshless  lower  jaw  in  A3,  the  large  mouth  curl  in  B3,  and 
the  flaring  subfix  in  A4,  which  are  the  essential  elements  of  the  head 
variants  for  the  cycle,  katun,  tun,  uinal,  and  kin,  respectively.  Com- 
pare these  glyphs  with  figures  25,  d-f,  27,  e-h,  29,  e-g,  31,  d-f,  and 
34,  e-g,  respectively.  The  coefficients  of  these  period  glyphs  are  all 
normal  forms  and  the  student  will  have  no  difficulty  in  reading  this 
number  as  9.14.19.8.0.2 

Reducing  this  by  means  of  Table  XIII  to  units  of  the  1st  order, 
we  have : 

A2=  9X144,000  =  1,296,000 
B2  =  14X  7,200=  100,800 
A3  =  19X  360=  6,840 
B3=  8X  20=  160 
A4=  OX  1=  0 

1,403,800 

Deducting  from  this  all  the  Calendar  Rounds  possible,  73  (see  Table 
XVI),  and  applying  rules  1  and  2  (pp.  139  and  140,  respectively),  to 
the  remainder,  the  day  reached  will  be  12  Ahau.  And  applying  rule  3 
(p.  141),  the  month  reached  will  be  18  Cumliu,  giving  for  the  terminal 
date  as  reached  by  calculation  12  Ahau  18  Cumliu.  The  day  should 
be  recorded  in  B4,  and  an  examination  of  this  glyph  shows  that  its 
coefficient  is  12,  the  day  coefficient  reached  by  calculation.  The 
glyph  itself,  however,  is  unlike  the  forms  for  Ahau  previously  encoun- 
tered in  plate  6,  A,  B5  and  0,  B4b,  and  in  plate  7,  A,  A7.  Turning 


1  The  full  text  of  this  inscription  is  given  in  Maudslay,  1889-1902:  i,  pis.  27-30. 

2  Note  the  decoration  on  the  numerical  bar. 


170 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


now  to  tha  forms  for  the  day  sign  Ahau  in  figure  16,  it  is  seen  that  the 
form  in  A4  resembles  the  third  variant  or  Ic',  the  grotesque  head,  and 
it  is  clear  that  the  day  12  Ahau  is  here  recorded.  At  first  sight  the  student 
might  think  that  the  month  glyph  follows  in  A5,  but  a  closer  inspection 
of  this  form  shows  that  this  is  not  the  case.  In  the  first  place,  since 
the  day  sign  is  Ahau  the  month  coefficient  must  be  either  3,  8,  13,  or 
18,  not  7,  as  recorded  (see  Table  VII),  and,  in  the  second  place,  the 
glyph  itself  in  A5  bears  no  resemblance  whatsoever  to  any  of  the 
month  signs  in  figure  19.  Consequently  the  month  part  of  the  Initial- 
series  terminal  date  of  this  text  should  follow  the  closing  glyph  of 
the  Supplementary  vSeries.  Following  along  the  glyphs  next  in  order, 
we  reach  in  A9  a  glyph  with  a  coefficient  9,  although  the  sign  itself 
bears  no  resemblance  to  the  month-glyph  ^indicators''  heretofore 
encountered  (see  fig.  65). 

The  glyph  following,  however,  in  A9b  is  quite  clearly  18  Cumhu  (see 
fig.  19,  g'-li'),  which  is  the  month  part  of  the  terminal  date  as  reached 
by  calculation.  Therefore,  since  A9a  has  the  coefficient  9  it  is  prob- 
able that  it  is  a  variant  of  the  month-glyph  ^indicator";  ^  and  con- 
sequently that  the  month  glyph  itself  follows,  as  we  have  seen,  in  B9. 
In  other  words,  the  terminal  date  recorded,  12  Ahau  18  Cumhu,  agrees 
with  the  terminal  date  reached  by  calculation,  and  the  whole  text, 
so  far  as  it  can  be  deciphered,  reads  9.14.19.8.0  12  Ahau  18  Cumhu. 
The  student  will  note  that  this  Initial  Series  precedes  the  Initial  Series 
in  plate  7,  A  by  exactly  10  uinals,  or  200  days.  Compare  A  and 
plate  7. 

In  plate  8,  A,  is  figured  the  Initial  Series  from  Stela  6  at  Copan.^ 
The  introducing  glyph  occupies  the  space  of  four  glyph-blocks, 
A1-B2,  and  there  follows  in  A3-B4a  the  Initial-series  number 
9.12.10.0.0.  The  cycle  glyph  in  A3  is  partially  effaced;  the  clasped 
hand,  however,  the  determining  characteristic  of  the  cycle  head, 
may  still  be  distinguished.  The  katun  head  in  B3  is  also  unmis- 
takable, as  it  has  the  same  superfix  as  in  the  normal  form  for  the 
katim.  At  first  sight  the  student  might  read  the  bar  and  dot  coeffi- 
cient as  14,  but  the  two  middle  crescents  are  purely  decorative  and 
have  no  numerical  value,  and  the  numeral  recorded  here  is  12  (see 
pp.  88-91).  Although  the  tun  and  uinal  period  glyphs  in  A4a 
and  A4b,^  respectively,  are  effaced,  their  coefficients  may  be  distin- 
guished as  10  and  0,  respectively.    In  such  a  case  the  student  is  per- 

1  So  far  as  known  to  the  writer,  this  very  unusual  variant  for  the  closing  glyph  of  the  Supplementary 
Series  occurs  in  but  two  other  inscriptions  ia  the  Maya  territory,  namely,  on  Stela  N  at  Copan.  See  pi.  26, 
Glyph  A14,  and  Inscription  6  of  the  Hieroglyphic  Stairway  at  Naranjo,  Glyph  Al  (?).  (Maler,  1908  b: 
pi.  27.) 

2  For  the  full  text  of  this  inscription  see  Maudslay,  1889-1902:  i,  pis.  105-107. 

3  In  this  glyph-block,  A4,  the  order  of  reading  is  irregular;  instead  of  passing  over  to  B4a  after  reading 
A4a  (the  10  tuns),  the  next  gl5T)h  to  be  read  is  the  sign  below  A4a,  A4b,  which  records  0  uinals,  and  only 
after  this  has  been  read  does  B4a  follow. 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57    PLATE  8 


A.    STELA  6,  COPAN  B.    STELA  9,  COPAN 


GLYPHS  REPRESENTING  INITIAL 
AND  DOT  NUMERALS  AND  H 


SERIES,  SHOWING  USE  OF  BAR 
EAD-VARIANT  PERIOD  GLYPHS 


MORLEY]      INTEODUCTION  TO  STUDY  OF  MAYA  HIEKOGLYPHS  171 


fectly  justified  in  assuming  that  the  tun  and  uinal  signs  originally 
stood  here.  In  B4a  the  kin  period  glyph  is  expressed  by  its  normal 
form  and  the  kin  coefficient  by  a  head-variant  numeral,  the  clasped 
hand  of  which  indicates  that  it  stands  for  0  (see  fig.  53,  s-w).^  The 
number  here  recorded  is  9.12.10.0.0. 

Reducing  this  to  units  of  the  1st  order  by  means  of  Table  XIII, 
we  have: 

A3=  9X144,000  =  1,296,000 

B3  =  12X  7,200=  86,400 
A4a  =  10X  360=  3,600 
A4b=  OX  20=  0 
B4a=  IX  0=  0 

1,  386,  000 

Deducting  from  this  number  all  the  Calendar  Rounds  possible,  73 
(see  Table  XVI),  and  applying  to  the  remainder  rules  1,  2,  and  3 
(pp.  139-141),  respectively,  the  date  reached  by  the  resulting  calcu- 
lations will  be  9  Ahau  18  Zotz.  Turning  to  our  text  again,  the  student 
will  have  little  difficulty  in  identifying  B4b  as  9  Ahau,  the  day  of  the 
above  terminal  date.  The  form  Ahau  here  recorded  is  the  grotesque 
head,  the  third  variant  or  Ic^  in  figure  16.  Following  the  next 
glyphs  in  order,  A5-A6,  the  closing  glyph  of  the  Supplementary 
Series  is  reached  in  B6a.  Compare  this  glyph  with  the  forms  in 
figure  65.  The  coefficient  of  B6a  is  again  a  head-variant  numeral,  as 
in  the  case  of  the  kin  period  glyph  in  B4a,  above.  The  fleshless  lower 
jaw  and  other  skull-like  characteristics  indicate  that  the  numeral  10 
is  here  recorded.  Compare  B6a  with  figure  52,  m-r.  Since  B6a  is 
the  last  glyph  of  the  Supplementary  Series,  the  next  glyph  B6b 
should  represent  the  month  sign.  By  comparing  the  latter  form 
with  the  month  signs  in  figure  19  the  student  will  readily  recognize 
that  the  sign  for  Zotz  in  e  or/ is  the  month  sign  here  recorded.  The 
coefficient  18  stands  above.  Consequently,  B4b  and  B6b  represent 
the  same  terminal  date,  9  Ahau  18  Zotz,  as  reached  by  calculation. 
This  whole  Initial  Series  reads  9.12.10.0.0  9  Ahau  18  Zotz,  and 
according  to  the  writer's  view,  the  monument  upon  which  it  occurs 
(Stela  6  at  Cop  an)  was  the  period  stone  for  the  ho  tun  which  began 
with  the  day  9.12.5.0.1  4  Imix  4  XuP  and  ended  with  the  day 
9.12.10.0.0  9  Ahau  18  Zotz,  here  recorded. 

In  plate  S,  B,  is  figured  the  Initial  Series  from  Stela  9  at  Copan.^ 
The  introducing  glyph  stands  in  A1-B2  and  is  followed  by  the  five 
period  glyphs  in  A3-A5.  The  cycle  is  very  clearly  recorded  in  A3, 
the  clasped  hand  being  of  a  particularly  realistic  form.  Although 

1  Texts  illustrating  the  head-variant  numerals  in  full  will  be  presented  later. 

2  The  preceding  hotun  ended  with  the  day  9.12.5.0.0  3  Ahau  3  Xul  and  therefore  the  opening  day  of  the 
next  hotun,  1  day  later,  will  be -9. 12.5.0.1  4  Imix  4  Xul. 

3  For  the  full  text  of  this  inscription,  see  Maudslay,  1889-1902:  i,  pis.  109,  110. 


172 


BUEEAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


the  coefficient  is  partially  effaced,  enough  remains  to  show  that  it 
was  above  5,  having  had  originally  more  than  the  one  bar  which 
remains,  and  less  than  11,  there  being  space  for  only  one  more  bar  or 
row  of  dots.  In  all  the  previous  Initial  Series  the  cycle  coefficient 
was  9,  consequently  it  is  reasonable  to  assume  that  4  dots  originally 
occupied  the  effaced  part  of  this  glyph.  If  the  use  of  9  cycles  in  this 
number  gives  a  terminal  date  which  agrees  with  the  terminal  date 
recorded,  the  above  assumption  becomes  a  certainty.  In  B3  six 
katuns  are  recorded.  Note  the  ornamental  dotted  ovals  on  each 
side  of  the  dot  in  the  numeral  6.  Although  the  head  for  the  tun  in 
A4  is  partially  effaced,  we  are  warranted  in  assuming  that  this  was 
the  period  originally  recorded  here.  The  coefficient  10  appears 
clearly.  The  uinal  head  in  B4  is  totally  unfamiliar  and  seems  to 
have  the  fleshless  lower  jaw  properly  belonging  to  the  tun  head; 
from  its  position,  however,  the  4th  in  the  number,  we  are  justified 
in  calling  this  glyph  the  uinal  sign.  Its  coefficient  denotes  that  0  uinals 
are  recorded  here.  Although  the  period  glyph  in  A5  is  also  entirely 
effaced,  the  coefficient  appears  clearly  as  0,  and  from  position  again, 
5th  in  the  number,  we  are  justified  once  more  in  assuming  that  0  kins 
were  originally  recorded  here.  It  seems  at  first  glance  that  the 
above  reading  of  the  number  A3-A5  rests  on  several  assumptions : 

1.  That  the  cycle  coefficient  was  originally  9. 

2.  That  the  effaced  glyph  in  A4  was  a  tun  head. 

3.  That  the  irregular  head  in  B4  is  a  uinal  head. 

4.  That  the  effaced  glyph  in  A5  was  a  kin  sign. 

The  last  three  are  really  certainties,  since  the  Maya  practice  in  record- 
ing Initial  Series  demanded  that  the  five  period  glyphs  requisite — 
the  cycle,  katun,  tim,  uinal,  and  kin — should  follow  each  other  in 
this  order,  and  in  no  other.  Hence,  although  the  3d,  4th,  and 
5th  glyphs  are  either  irregular  or  effaced,  they  must  have  been  the 
tun,  uinal,  and  kin  signs,  respectively.  Indeed,  the  only  important 
assumption  consisted  in  arbitrarily  designating  the  cycle  coefficient 
9,  when,  so  far  as  the  appearance  of  A3  is  concerned,  it  might  have 
been  either  6,  7,  8,  9,  or  10.  The  reason  for  choosing  9  rests  on  the 
overwhelming  evidence  of  antecedent  probability.  Moreover,  as 
stated  above,  if  the  terminal  date  recorded  agrees  with  the  terminal 
date  determined  by  calculation,  using  the  cycle  coefficient  as  9,  our 
assumption  becomes  a  certainty.  Designating  the  above  number  as 
9.6.10.0.0  then  and  reducing  this  by  means  of  Table  XIII,  we  obtain: 

A3=  9X144,000  =  1,296,000 

B3=  6X    7,200=  43,200 

A4  =  10X        360=  3,600 

B4=  OX         30=  0 

A5=  OX  1=  0 


1,  342,  800 


MORLBY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEEOGLYPHS  173 


Deducting  from  this  number  all  the  Calendar  Rounds  possible,  70 
(see  Table  XVI);  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and  141, 
respectively)  to  the  rem^ainder,  the  date  determined  by  the  resulting 
calculations  will  be  8  Ahau  13  Pax.  Turning  to  our  text  again,  the 
student  will  have  little  difficulty  in  recognizing  the  first  part  of  this 
date,  the  day  8  Ahau,  in  B5.  The  numeral  8  appears  clearly,  and  the 
day  sign  is  the  profile-head  V  or  i' ,  the  second  variant  for  Ahau  in 
figure  16.  The  significance  of  the  element  standing  between  the 
numeral  and  the  day  sign  is  imknown.  Following  along  through 
A6,  B6,  A7,  B7,  the  closing  glyph  of  the  Supplementary  Series  is 
reached  in  A8.  The  glyph  itself  is  on  the  left  and  the  coefficient,  here 
expressed  by  a  head  variant,  is  on  the  right.  The  student  will  have 
no  difficulty  in  recognizing  the  glyph  and  its  coefficient  by  comparing 
the  former  with  figure  65,  and  the  latter  with  the  head  variant  for 
10  in  figure  52,  m-r.  Note  the  fleshless  lower  j  aw  in  the  head  numeral 
in  both  places.  The  following  glyph,  B8,  is  one  of  the  clearest  in 
the  entire  text.  The  numeral  is  13,  and  the  month  sign  on  comparison 
with  figure  19  unmistakably  proves  itself  to  be  the  sign  for  Pax  in  c' . 
Therefore  the  terminal  date  recorded  in  B5;  B8,  namely,  8  Ahau  13 
Pax,  agrees  with  the  terminal  date  determined  by  calculation;  it  fol- 
lows, further,  that  the  effaced  cycle  coefficient  in  A3  must  have  been  9, 
the  value  tentatively  ascribed  to  it  in  the  above  calculations.  The 
whole  Initial  Series  reads  9.6.10.0.0  8  Aha-u  13  Pax. 

Some  of  the  peculiarities  of  the  numerals  and  signs  in  this  text  are 
doubtless  due  to  its  very  great  antiquity,  for  the  monument  presenting 
this  inscription,  Stela  9,  records  the  next  to  earliest  Initial  Series  ^ 
yet  deciphered  at  Copan.^  Evidences  of  antiquity  appear  in  the 
glyphs  in  several  different  ways.  The  bars  denoting  5  have  square 
ends  and  all  show  considerable  ornamentation.  This  type  of  bar 
was  an  early  manifestation  and  gave  way  in  later  times  to  more 
rounded  forms.  The  dots  also  show  this  greater  ornamentation, 
which  is  reflected,  too,  by  the  signs  themselves.  The  head  forms  show 
greater  attention  to  detail,  giving  the  whole  glyph  a  more  ornate 
appearance.  All  this  embellishment  gave  Way  in  later  times  to  more 
simplified  forms,  and  we  have  represented  in  this  text  a  stage  in  glyph 
morphology  before  conventionalization  had  worn  down  the  different 
signs  to  little  more  than  their  essential  elements. 

In  figure  68,  A,  is  figured  the  Initial  Series  on  the  west  side  of  Stela 
C  at  Quirigua.^  The  introducing  glyph  in  A1-B2  is  followed  by  the 
number  in  A3-A5,  which  the  student  will  have  no  difficulty  in  reading 

1  The  oldest  Initial  Series  at  Copan  is  recorded  on  Stela  15,  which  is  40  years  older  than  Stela  9.  For  a 
discussion  of  this  text  see  pp.  187,  188. 

2  An  exception  to  this  statement  should  be  noted  in  an  Initial  Series  on  the  Hieroglyphic  Stairway, 
which  records  the  date  9.5.19.3.0  8  Ahau  3  Zotz.  The  above  remark  applies  only  to  the  large  monuments, 
which,  the  writer  believes,  were  period-markers.  Stela  9  is  therefore  the  next  to  the  oldest  "period  stone" 
yet  discovered  at  Copan.  It  is  more  than  likely,  however,  that  there  are  several  older  ones  as  yet  unde- 
clphered. 

3  For  the  full  text  of  this  inscription,  see  Maudslay,  1889-1902:  ii,  pis.  17-19, 


174 


BUREAU  OF  AMEEICAN  ETHNOLOGY 


[bull.  57 


except  for  the  head-variant  numeral  attached  to  the  kin  sign  in  A5. 
The  clasped  hand  in  this  glyph,  however,  suggests  that  0  kins  are 
recorded  here,  and  a  comparison  of  this  form  with  figure  53,  s-w,  con- 
firms the  suggestion.    The  number  therefore  reads  9.1.0.0.0.  Re- 


FiG.  68.  Initial  Series  showing  bar  and  dot  numerals  and  head-variant  period  glyphs:  A,  Stela  C  (west 
side),  Quirigua;  B,  Stela  M,  Copan. 

ducing  this  number  by  means  of  Table  XIII  to  units  of  the  1st  order, 
we  obtain: 

A3  =  9  X  144,  000  1,  296,  000 
B3  =  1X  7,200=  7,200 
A4=0X  360=  0 
B4  =  0X  20=  0 
A5  =  0X  1=  0 

1,  303;  200 

Deducting  from  this  number  all  the  Calendar  Rounds  possible,  68 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and  141, 
respectively)  to  the  remainder,  we  reach  for  the  terminal  date  6  Ahau 
13  Yaxkin.  Looking  for  the  day  part  of  this  date  in  B5,  we  find  that 
the  form  there  recorded  bears  no  resemblance  to  6  Ahau,  the  day 
determined  by  calculation.  Moreover,  comparison  of  it  with  the  day 
signs  in  figure  16  shows  that  it  is  unlike  all  of  them;  further,  there  is 


MOELEY]      INTKODUCTIOlSr  TO  STUDY  OF  MAYA  HIEROGLYPHS 


175 


no  bar  and  dot  coefficient.  These  several  points  indicate  that  the 
day  sign  is  not  the  glyph  in  B5,  also  that  the  day  sign  is,  therefore, 
out  of  its  regular  position.  The  next  glyph  in  the  text,  A6,  instead 
of  being  one  of  the  Supplementary  Series  is  the  day  glyph  6  Ahau, 
which  should  have  been  recorded  in  B5.  The  student  will  readily 
make  the  same  identification  after  comparing  A6  with  figure  16,  e'-g' . 
A  glance  at  the  remainder  of  the  text  will  show  that  no  Supplementary 
Series  is  recorded,  and  consequently  that  the  month  glyph  will  be 
found  immediately  following  the  day  glyph  in  B6.  The  form  in  B6 
has  a  coefficient  13,  one  of  the  four  (3,  8,  13,  18)  which  the  month 
must  have,  since  the  day  sign  is  Ahau  (see  Table  VII) .  A  com.parison 
of  the  form  in  B6  with  the  month  signs  in  figure  19  shows  that  the 
month  Yaxkin  in  or  Z  is  the  form  here  recorded;  therefore  the  ter- 
minal date  recorded  agrees  with  the  terminal  date  reached  by  calcu- 
lation, and  the  text  reads  9.1.0.0.0  6  Ahau  IS  Yaxkin.^ 

In  figure  68,  B,  is  shown  the  Initial  Series  on  Stela  M  at  Copan.^ 
The  introducing  glyph  appears  in  Al  and  the  Initial-series  number 
in  Bla-B2a.  The  student  will  note  the  use  of  both  normal -form  and 
head-variant  period  glyphs  in  this  text,  the  cycle,  tun,  and  uinal  in 
Bla,  A2a,  and  A2b,  respectively,  being  expressed  by  the  latter,  and 
the  katun  and  kin  in  Bib  and  B2a,  respectively,  by  the  former.  The 
number  recorded  is  9.16.5.0.0,  and  this  reduces  to  units  of  the  first 
order,  as  follows  (see  Table  XIII) : 

Bla=  9X144,  000  =  1,296,  000 
Blb  =  16x  7,200=  115;  200 
A2a=  5X  360=  1,800 
A2b=  Ox  20=  0 
B2a=  Ox  1=  0 

1,413,000 

Deducting  from  this  number  all  the  Calendar  Rounds  possible,  74 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and  141, 
respectively)  to  the  remainder,  the  terminal  date  reached  by  the 
resulting  calculations  will  be  8  Ahau  8  Zotz.  Turning  to  our  text,  the 
student  will  have  no  difficulty  in  recognizing  in  B2b  the  day  8  Ahau. 
The  month  glyph  in  this  inscription  irregularly  follows  immediately 

1  Although  this  date  is  considerably  older  than  that  on  Stela  9  at  Copan,  its  several  glyphs  present  none 
of  the  marks  of  antiquity  noted  in  connection  with  the  preceding  example  (pi.  8,  B).  For  example,  the  ends 
of  the  bars  denoting  5  are  not  square  but  round,  and  the  head-variant  period  gljTphs  do  not  shoAv  the 
same  elaborate  and  ornate  treatment  as  in  the  Copan  text.  This  apparent  contradiction  permits  of  an 
easy  explanation.  Although  the  Initial  Series  on  the  west  side  of  Stela  C  at  Quirigua  undoubtedly  refers 
to  an  earlier  date  than  the  Initial  Series  on  the  Copan  monument,  it  does  not  follow  that  the  Quirigua 
monument  is  the  older  of  the  two.  This  is  true  because  on  the  other  side  of  this  same  stela  at  Quirigua 
Is  recorded  another  date,  9.17.5.0.0  6  Ahau  13  Kayab,  more  than  three  hundred  years  later  than  the  Initial 
Series  9.1.0.0.0  6  Ahau  13  Yaxkin  on  the  west  side,  and  this  later  date  is  doubtless  the  one  which  referred 
to  present  time  when  this  monument  was  erected.  Therefore  the  Initial  Series  9.1.0.0.0  6  Ahau  13  Yaxkin 
does  not  represent  the  period  which  Stela  C  was  erected  to  mark,  but  some  far  earlier  date  in  Maya 
history. 

2  For  the  full  text  of  this  inscription  see  Maudslay,  1889-1902:  i,  pi.  74. 


176  BUREAU  OF  AMEEICAN  ETHNOLOGY  [bull.  57 

the  day  glyph.  Compare  the  form  in  A3a  with  the  month  signs  in 
figure  19  and  it  will  be  found  to  be  the  sign  for  Zotz  (see  fig.  19,  e-f). 
The  coefiicient  is  8  and  the  whole  glyph  represents  the  month  part 
8  Zotz,  the  same  as  determined  by  calculation.  This  whole  Initial 
Series  reads  9.16.5.0.0  8  Ahau  8  Zotz. 

The  Maya  texts  presented  up  to  this  point  have  all  been  drawings 
of  originals,  which  are  somewhat  easier  to  make  out  than  either 
photographs  of  the  originals  or  the  originals  themselves.  However, 
in  order  to  familiarize  the  student  with  photographic  reproductions 
of  Maya  texts  a  few  will  be  inserted  here  illustrating  the  use  of  bar 
and  dot  numerals  with  both  normal-form  and  head-variant  period 
glyphs,  with  which  the  student  should  be  perfectly  familiar  by  this 
time. 

In  plate  9,  ^,  is  figured  a  photograph  of  the  Initial  Series  on  the  front 
of  Stela  11  at  Yaxchilan.^  The  introducing  glyph  appears  in  Al  Bl ;  9 
cycles  in  A2 ;  16  katuns  in  B2,  1  tun  in  A3,  0  uinals  in  B3,  and  0  kins  in 
B4.  The  student  will  note  the  clasped  hand  in  the  cycle  head,  the  oval 
in  the  top  of  the  katun  head,  the  large  mouth  curl  in  the  uinal  head, 
and  the  flaring  postfix  in  the  kin  head.  The  tun  is  expressed  by  its 
normal  form.  The  number  here  recorded  is  9.16.1.0.0,  and  reducing 
this  to  units  of  the  first  order  by  means  of  Table  XIII,  we  have: 

A2=  9X144,  000  =  1;  296,  000 
B2  =  16X  7,200=  115,200 
A3=  IX  360=  360 
B3=  Ox  20=  0 
A4=  Ox  1=  0 

1,411,560 

Deducting  from  this  nimiber  all  the  Calendar  Eounds  possible,  74 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and 
141,  respectively),  to  the  remainder,  the  terminal  date  reached  by  the 
resulting  calculations  will  be  11  Ahau  8  Tzec.  The  day  part  of  this 
date  is  very  clearly  recorded  in  B4  immediately  after  the  last  period 
glyph,  and  the  student  will  readily  recognize  the  day  11  Ahau  in  this 
form.  Following  along  the  glyphs  of  the  Supplementary  Series  in 
CI  Dl,  C2  D2,  the  closing  glyph  is  reached  in  C3b.  It  is  very  clear 
and  has  a  coefiicient  of  9.  The  glyph  following  (D3)  should  record 
the  month  sign.  A  comparison  of  this  form  with  the  several  month 
signs  in  figure  19  shows  that  Tzec  is  the  month  here  recorded.  Com- 
pare D3  with  figure  19,  g-li.  The  month  coefficient  is  8.  The  ter- 
minal date,  therefore,  recorded  in  B4  and  D3  (11  Ahau  8  Tzec)  agrees 
with  the  terminal  date  determined  by  calculation,  and  this  whole  text 
reads  9.16.1.0.0   11  Ahau  8  Tzec.    The  meaning  of  the  element 


1  For  the  full  text  of  this  inscription  see  Maler,  1903:  n,  No.  2,  pis.  74,  75. 


BUREAU  OF  AMERICAN  ETHNOLOGY  BULLETIN  57  PLATE 


A.    STELA  11,  YAXCHILAN 


B.    ALTAR  IN  FRONT  OF  STRUCTURE  44,  YAXCHILAN 


GLYPHS  REPRESENTING  INITIAL  SERIES,  SHOWING  USE 
OF  BAR  AND  DOT  NUMERALS  AND  HEAD-VARIANT 
PERIOD  GLYPHS 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


177 


between  the  tun  coefficient  and  the  tun  sign  in  A3,  which  is  repeated 
again  in  D3  between,  the  month  coefficient  and  the  month  sign,  is 
unknown. 

In  plate  9,  B,  is  figured  the  Initial  Series  on  an  altar  in  front  of 
Structure  44  at  Yaxchilan.^  The  introducing  glyph  appears  in  Al  Bl 
and  is  followed  by  the  number  in  A2-A4.  The  period  glyphs  are  all 
expressed  as  head  variants  and  the  coefficients  as  bar  and  dot  numerals. 
Excepting  the  kin  coefficient  in  A4,  the  number  is  quite  easily  read 
as  9.12.8.14.  ?  An  inspection  of  our  text  shows  that  the  coefficient 
must  be  0,  1,  2,  or  8.  Let  us  work  out  the  terminal  dates  for  all  four 
of  these  values,  commencing  with  0,  and  then  see  which  of  the  result- 
ing terminal  days  is  the  one  actually  recorded  in  A4.  Reducing  the 
number  9.12.8.14.0  to  units  of  the  first  order  by  means  of  Table 
XIII,  we  have: 

A2=  9X144,000  =  1,296,000 
B2  =  12X  7,200=  86,400 
A3=  8X  360=  2,880 
B3  =  14X  20=  280 
A4=  Ox  1=  0 


1,  385,  560 

Deducting  from  this  number  all  the  Calendar  Rounds  possible,  73 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and 
141,  respectively),  to  the  remainder,  the  terminal  day  reached  will  be 
11  Aliau  3  Pop.  Therefore  the  Initial-series  numbers  9.12.8.14.1, 
9.12.8.14.2,  and  9.12.8.14.3  will  lead  to  the  three  days  immediately  fol- 
lowing 9. 12.8. 14.0  11  Ahau  3  Pop.  Therefore  our  four  possible  termi- 
nal dates  will  be: 

9.12.8.14.0  11  Ahau  3  Pop 

9.12.8.14.1  12  Imix  4  Pop 

9.12.8.14.2  13  Ik       5  Pop 

9.12.8.14.3  1  Akbal  6  Pop 

Now  let  us  look  for  one  of  these  four  terminal  dates  in  the  text.  The 
day  reached  by  an  Initial  Series  is  almost  invariably  recorded  imme- 
diately after  the  last  period  glyph;  therefore,  if  this  inscription  is 
regular,  the  day  glyph  should  be  B4.  This  glyph  probably  has  the 
coefficient  12  (2  bars  and  2  numerical  dots),  the  oblong  element 
between  probably  being  ornamental  only.  This  number  must  be 
either  11  or  12,  since  if  it  were  13  the  3  dots  would  all  be  of  the  same 
size,  which  is  not  the  case.  An  inspection  of  the  coefficient  in  B4 
eliminates  from  consideration,  therefore,  the  last  tw^o  of  the  above 
four  possible  terminal  dates,  and  reduces  the  possible  values  for  the 
kin  coefficient  in  A4  to  0  or  1.  Comparing  the  glyph  in  B4  with  the 
day  signs  in  figure  16,  the  form  here  recorded  will  be  found  to  be  iden- 
tical with  the  sign  for  Imix  in  figure  16,  a.  This  eliminates  the  first 
terminal  date  above  and  leaves  the  second,  the  day  part  of  which 

1  For  the  full  text  of  this  inscription  see  Maler,  1903:  ii,  No.  2,  pi.  79,  2. 
43508°— Bull.  57—15  12 


178 


BUREAU  OF  AMEBIC  AN  ETHNOLOGY 


[bull.  57 


we  have  just  seen  appears  in  B4.  This  further  proves  that  the  kin 
coefficient  in  A4  is  1.  The  final  confirmation  of  this  identification 
will  come  from  the  month  glyph,  which  must  be  4  Pop  if  we  have 
correctly  identified  the  day  as  12  Imix.  If,  on  the  other  hand,  the 
day  were  11  Ahau,  the  month  glyph  would  be  3  Pop.  Passing  over 
A5  B5,  A6  B6,  Cl  Dl,  and  C2,  we  reach  in  D2a  the  closing  glyph 
of  the  Supplementary  Series,  here  showing  the  coefficient  9.  Com- 
pare this  form  with  figure  65.  The  month  gl3^ph,  therefore,  should 
appear  in  D2b.  The  coefficient  of  this  glyph  is  very  clearly  4,  thus 
confirming  our  identification  of  B4  as  12  Imix.  (See  Table  VIL) 
And  finally,  the  month  glyph  itself  is  Pop.  Compare  D2b  with 
figure  19,  a.  The  whole  Initial  Series  in  plate  9,  B,  therefore  reads 
9.12.8.14.1  12  Imix  4  Pop. 

In  plate  10,  is  figured  the  Initial  Series  from  Stela  3  at  Tikal.* 
The  introducing  glyph,  though  somewhat  effaced,  may  still  be  rec- 
ognized in  Al.  The  Initial-series  number  follows  in  B1-B3.  The 
head-variant  period  glyphs  are  too  badly  weathered  to  show  the 
determining  characteristic  in  each  case,  except  the  uinal  head  in  A3, 
the  mouth  curl  of  which  appears  clearly,  and  their  identification  rests 
on  their  relative  positions  with  reference  to  the  introducing  glyph. 
The  reliability  of  this  basis  of  identification  for  the  period  glyphs  of 
Initial  Series  has  been  thoroughly  tested  in  the  texts  already  pre- 
sented and  is  further  confirmed  in  this  very  inscription  by  the  uinal 
head.  Even  if  the  large  mouth  curl  of  the  head  in  A3  had  not  proved 
that  the  uinal  was  recorded  here,  we  should  have  assumed  this  to  be 
the  case  because  this  glyph,  A3,  is  the  fourth  from  the  introducing 
glyph.  The  presence  of  the  mouth  curl  therefore  confirms  the  iden- 
tification based  on  position.  The  student  will  have  no  difficulty  in 
reading  the  number  recorded  in  B1-B3  as  9.2.13.0.0. 

Reducing  this  number  by  means  of  Table  XIII  to  units  of  the  first 
order,  we  obtain: 

Bl=  9X144,  000  =  1,296,  000 
A2=  2X  7,200=  14,400 
B2  =  13x  360=  4,680 
A3=  OX  20=  0 
B3=  OX  1=  0 

1,  315,  080 

Deducting  all  the  Calendar  Roimds  possible  from  this  number,  69 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and 
141,  respectively)  to  the  remainder,  the  terminal  date  reached  will 
be  4  Ahau  13  Kayab.  It  remains  to  find  this  date  in  the  text.  The 
glyph  in  A4,  the  proper  position  for  the  day  glyph,  is  somewhat 
effaced,  though  the  profile  of  the  human  head  may  yet  be  traced, 
thus  enabling  us  to  identify  this  form  as  the  day  sign  Ahau.  Com- 


1  For  the  full  text  of  this  inscription  see  Maler,  1911:  v,  No.  1,  pi.  15. 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57    PLATE  10 


GLYPHS  REPRESENTING  INITIAL  SERIES,  SHOW- 
ING USE  OF  BAR  AND  DOT  NUMERALS  AND 
HEAD-VARIANT  PERIOD  GLYPHS-STELA  3, 
TIKAL 


A  (EAST  SIDE),  QUIRIGUA 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  179 


pare  figure  16,  ti' ,  i' .  The  coefficient  of  A4  is  very  clearly  4  dots, 
that  is,  4,  and  consequently  this  glyph  agrees  with  the  day  as  de- 
termined by  calculation,  4  Ahau.  Passing  over  B4,  A5.,  B5,  and  A6, 
we  reach  in  B6  the  closing  glyph  of  the  Supplementary  Series,  here 
recorded  with  a  coefficient  of  9.  Compare  B6  with  figure  65.  The 
month  glyph  follows  in  A7  with  the  coefficient  13.  Comparing  this 
latter  glyph  with  the  month  signs  in  figure  19,  it  is  evident  that  the 
month  Kayab  (fig.  19,  dJ-f)  is  recorded  in  A7,  which  reads,  therefore, 
13  Kayab.  Hence  the  whole  text  records  the  Initial  Series  9.2.13.0.0 
4  Ahau  13  Kayab. 

This  Initial  Series  is  extremely  important,  because  it  records  the 
earliest  contemporaneous  ^  date  yet  found  on  a  monument  ^  in  the 
Maya  territory. 

In  plate  11  is  figured  the  Initial  Series  from  the  east  side  of  Stela  A 
at  Quirigua.  ^  The  introducing  glyph  appears  in  A1-B2  and  the 
Initial-series  number  in  A3-A5.  The  student  will  have  little  diffi- 
culty in  picking  out  the  clasped  hand  in  A3,  the  oval  in  the  top  of 
the  head  in  B3,  the  fleshless  lower  jaw  in  A4,  the  mouth  curl  in  B4, 
as  the  essential  characteristic  of  the  cycle,  katun,  tun,  and  uinal 
heads,  respectively.  The  kin  head  in  A5  is  the  banded-headdress 
variant  (compare  fig.  34,  ^,  j),  and  this  completes  the  number,  which 
is  9.17.5.0.0.  Reducing  this  by  m_eans  of  Table  XIII  to  units  of  the 
first  order,  we  have : 


A3  = 

9  X  144, 

000  =  1, 

296, 

000 

B3  = 

17  X  7, 

200- 

122, 

400 

A4  = 

5X 

360  = 

800 

B4  = 

Ox 

20  = 

0 

A5  = 

OX 

0  = 

0 

1, 

420, 

200 

Deducting  from  this  number  all  the  Calendar  Rounds  possible,  73 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and  141, 


1  As  used  throughout  this  book,  the  expression  "the  contemporaneous  date"  designates  the  time  when 
the  monument  on  which  such  a  date  is  found  was  put  into  formal  use,  that  is,  the  time  of  its  erection.  As 
will  appear  later  in  the  discussion  of  the  Secondary  Series,  many  monuments  present  several  dates  between 
the  extremes  of  which  elapse  long  periods.  Obviously,  only  one  of  the  dates  thus  recorded  can  represent 
the  time  at  which  the  monument  was  erected.  In  such  inscriptions  the  final  date  is  almost  invariably 
the  one  designating  contemporaneous  time,  and  the  earlier  dates  refer  probably  to  historical,  traditional, 
or  even  mythological  e  vents  in  the  Maya  past.  Thus  the  Initial  Series  9.0.19.2.4  2  Kan  2  Yax  on  Lintel  21 
at  Yaxchilan,  9.1.0.0.0  6  Ahau  13  Yaxkin  on  the  west  side  of  Stela  C  at  Quirigua,  and  9.4.0.0.0  13  Ahau  18 
Yax  from  the  Temple  of  the  Inscriptions  at  Palenque,  all  refer  probably  to  earlier  historical  or  traditional 
events  in  the  past  of  these  three  cities,  but  they  do  not  indicate  the  dates  at  which  they  were  severally 
recorded.  As  Initial  Series  which  refer  to  purely  mythological  events  may  be  classed  the  Initial  Series 
from  the  Temples  of  the  Sun,  Cross,  and  Foliated  Cross  at  Palenque,  and  from  the  east  side  of  Stela  C  at 
Quirigua,  all  of  which  are  concerned  with  dates  centering  around  or  at  the  beginning  of  Maya  chronology. 
Stela  3  at  Tikal  (the  text  here  under  discussion),  on  the  other  hand,  has  but  one  date,  which  probably 
refers  to  the  time  of  its  erection,  and  is  therefore  contemporaneous. 

2  There  are  one  or  two  earlier  Initial  Series  which  probably  record  contemporaneous  dates;  these  are  not 
inscribed  on  large  stone  monuments  but  on  smaller  antiquities,  namely,  the  Tuxtla  Statuette  and  the 
Leyden  Plate.    For  the  discussion  of  these  early  contemporaneous  Initial  Series,  see  pp.  194-198. 

3  For  the  full  text  of  this  inscription  see  Maudslay,  1889-1902:  n,  pis.  4-7. 


180 


BUEEAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


respectively)  to  the  remainder,  the  terminal  day  reached  will  be 
found  to  be  6  Ahau  13  Kayab. 

In  B5  the  profile  variant  of  the  day  sign,  Ahau,  is  clearly  recorded 
(fig.  16,  h' ,  i'),  and  to  it  is  attached  a  head-variant  numeral.  Com- 
paring this  with  the  head-variant  numerals  in  figures  51-53,  the  stu- 
dent will  have  little  difficulty  in  identifying  it  as  the  head  for  6  (see 
fig.  51,  t-^).  Note  the  so-called  hatchet  eye"  in  A5,  which  is  the 
determining  characteristic  of  the  head  for  6  (see  p.  99).  Passing 
over  A6  B6,  A7  B7,  AS  B8,  we  reach  in  A9  the  closing  glyph  of 
the  Supplementary  Series,  here  showing  the  head-variant  coefficient 
10  (see  fig.  52,  m-r).  In  B9,  the  next  glyph,  is  recorded  the  month 
13  Kayab  (see  fig.  19,  d'-f).  The  whole  Initial  Series  therefore 
reads  9.17.5.0.0  6  Ahau  13  Kayab, 

All  the  Initial  Series  heretofore  presented  have  had  normal-form 
numerals  with  the  exception  of  an  incidental  head-variant  number 
here  and  there.  By  this  time  the  student  should  have  become  thor- 
oughly familiar  with  the  use  of  bar  and  dot  numerals  in  the  inscrip- 
tions and  should  be  ready  for  the  presentation  of  texts  showing  head- 
variant  numerals,  a  more  difficult  group  of  glyphs  to  identify. 

In  plate  12,  A,  is  figured  the  Initial  Series  on  the  tablet  from  the 
Temple  of  the  Foliated  Cross  at  Palenque.^  The  introducing  glyph 
appears  in  Al  B2,  and  is  followed  by  the  Initial-series  number  in 
A3-B7.  The  student  will  have  little  difficulty  in  identifying  the  heads 
in  B3,  B4,  B5,  B6,  and  B7  as  the  head  variants  for  the  cycle,  katun, 
tun,  uinal,  and  kin,  respectively.  The  head  in  A3  prefixed  to  the 
cycle  glyph  in  B3  has  for  its  determining  characteristic  the  forehead 
ornament  composed  of  more  than  one  fart  (here,  of  two  parts).  As 
explained  on  page  97,  this  is  the  essential  element  of  the  head  for  1. 
Compare  A3  with  figure  51,  a-e,  and  the  two  glyphs  will  be  found  to 
be  identical.  We  may  conclude,  therefore,  that  in  place  of  the  usual 
9  cycles  heretofore  encountered  in  Initial  Series,  we  have  recorded 
in  A3-B3  1  cycle.^  The  katun  coefficient  in  A4  resembles  closely  the 
cycle  coefficient  except  that  its  forehead  ornament  is  composed  of 
but  a  single  part,  a  large  curl.  As  explained  on  page  97,  the  heads 
for  1  and  8  are  very  similar,  and  are  to  be  distinguished  from  each 
other  only  by  their  forehead  ornaments,  the  former  having  a  forehead 
ornament  composed  of  more  than  one  part,  as  in  A3,  and  the  latter 
a  forehead  ornament  composed  of  but  one  part,  as  here  in  A4.  This 
head,  moreover,  is  very  similar  to  the  head  for  8  in  figure  52,  a-f; 
indeed,  the  only  difference  is  that  the  former  has  a  fleshless  lower 
jaw.  This  is  the  essential  element  of  the  head  for  10  (see  p.  100); 
when  applied  to  the  head  for  any  other  numeral  it  increases  the 
value  of  the  resulting  head  by  10.    Therefore  we  have  recorded  in 

1  For  the  full  text  of  this  inscription  see  Maudslay,  1889-1902:  iv,  pis.  80-82. 

2  As  explained  on  p.  179,  footnote  1,  this  Initial  Series  refers  probably  to  some  mythological  event  rather 
than  to  any  historical  occurrence.  The  date  here  recorded  precedes  the  historic  period  of  the  Maya  civili- 
zation by  upward  of  3,000  years. 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  181 


A4  B4,  18  (8  +  10)  katuns.  The  tun  coefficient  in  A5  has  for  its 
determining  characteristic  the  tun  headdress,  which,  as  explained  on 
page  99,  is  the  essential  element  of  the  head  for  5  (see  fig.  51,  n-s). 
Therefore  A5  represents  5,  and  A5  B5,  5  tuns.  The  uinal  coefficient 
in  A6  has  for  its  essential  elements  the  large  bulging  eye,  square  irid, 
and  snaglike  front  tooth.  As  stated  on  page  98,  these  characterize 
the  head  for  4,  examples  of  which  are  given  in  figure  51,  j-m.  Con- 
sequently, A6  B6  records  4  uinals.  The  kin  coefficient  in  A7  is  quite 
clearly  0.  The  student  will  readily  recognize  the  clasped  hand,  which 
is  the  determining  characteristic  of  the  0  head  (see  p.  101  and  fig.  53, 
s-w).  The  number  recorded  in  A3-B7  is,  therefore,  1.18.5.4.0. 
Reducing  this  number  to  units  of  the  1st  order  by  means  of  Table 
Xin,  we  obtain: 

A3B3=  1  X144,000  =  144,000 
A4B4  =  18  X  7,  200  =  129.  600 
A5B5=  5X  360=  1,800 
A6B6=  4X  20=  80 
A7B7=  OX  1=  0 

275,  480 

Deducting  from  this  number  all  the  Calendar  Rounds  possible,  14 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and 
141,  respectively),  the  terminal  date  reached  will  be  1  Ahau  13  Mac. 
Of  this  date,  the  day  part^  1  Ahau,  is  recorded  very  clearly  in  A8  B8. 
Compare  the  head  in  A8  with  the  head  in  A3,  which,  we  have  seen, 
stood  for  1  and  also  with  figure  51,  a-e,  and  the  head  in  B8  with 
figure  16,  li^,  i' ,  the  profile  head  for  the  day  sign  Ahau.  This  text  is 
irregular  in  that  the  month  glyph  follows  immediately  the  day  glyph, 
i.  e. ,  in  A9.  The  glyph  in  A9  has  a  coefficient  13,  which  agrees  with  the 
month  coefficient  determined  by  calculation,  and  a  comparison  of  B9 
with  the  forms  for  the  months  in  figure  19  shows  that  the  month 
Mac  (fig.  19,  x)  is  here  recorded.  The  whole  Initial  Series  there- 
fore reads  1.18.5.4.0  1  Ahau  13  Mac. 

In  plate  12,  is  figured  the  Initial  Series  on  the  tablet  from  the 
Temple  of  the  Sun  at  Palenque.^  The  introducing  glyph  appears  in 
A1-B2  and  is  followed  by  the  Initial-serie.^  number  in  A3-B7.  The 
student  will  have  no  difficulty  in  identifying  the  period  glyphs  in 
B3,  B4,  B5,  B6,  and  B7;  and  the  cycle,  katun,  and  tun  coefficients 
in  A3,  A4,  and  A5,  respectively,  will  be  found  to  be  exactly  hke  the 
corresponding  coefficients  in  the  preceding  Initial  Series  (pi.  12,  ^, 
A3,  A4,  A5),  which,  as  we  have  seen,  record  the  numbers  1,  18,  and 
5,  respectively.  The  uinal  coefficient  in  A6,  however,  presents  a 
new  form.  Here  the  determining  characteristic  is  the  banded  head- 
dress, or  ffilet,  which  distinguishes  the  head  for  3,  as  explained  on 
page  98  (see  fig.  51  li,  i).    We  have  then  in  A6  B6  record  of  3 


1  For  the  fvill  text  of  this  inscription  see  Maudslay,  1889-1902;  iv,  pis.  87-89. 


182 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


uinals.  The  kin  coefficient  in  A7  is  very  clearly  6.  Note  the  ' '  hatchet 
eye,"  which,  as  explained  on  page  99,  is  the  essential  element  of 
this  head  numeral,  and  also  compare  it  with  figure  51,  t-v.  The 
number  recorded  in  A3-B7  therefore  is  1.18.5.3.6.  Reducing  this  to 
units  of  the  first  order  by  means  of  Table  XIII,  we  obtain: 

A3B3=  1X144,000  =  144,000 
A4B4  =  18X  7,200  =  129,600 
A5B5=  5X  360=  1,800 
A6B6=  3X  20=  60 
A7B7=  6x  1=  6 

275,  466 

Deducting  from  this  number  all  the  Calendar  Rounds  possible,  14 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and 
141),  respectively,  to  the  remainder,  the  terminal  date  reached  will 
be  13  Cimi  19  Ceh.  If  this  inscription  is  regular,  the  day  part  of  the 
above  date  should  follow  in  A8  B8,  the  former  expressing  the  coeffi- 
cient and  the  latter  the  day  sign.  Comparing  A8  with  the  head 
numerals  in  figures  51-53,  it  will  be  foimd  to  be  like  the  second 
variant  for  13  in  figure  52,  x-V ,  the  essential  element  of  which  seems 
to  be  the  pendulous  nose  surmounted  by  a  curl,  the  protruding 
mouth  fang,  and  the  large  bulging  eye.  Comparing  the  glyph  in  B8 
with  the  day  signs  in  figure  16,  it  will  be  seen  that  the  form  here 
recorded  is  the  day  sign  Cimi  (fig.  16,  Ti,  i).  Therefore  A8  B8 
expresses  the  day  13  Cimi.  The  month  glyph  is  recorded  very 
irregularly  in  this  text,  since  it  occurs  neither  immediately  after  the 
Supplementary  Series  or  the  day  sign,  but  the  second  glyph  after  the 
day  sign,  in  B9.  A  comparison  of  this  form  with  figure  19,  u-v, 
shows  that  the  month  Ceh  is  recorded  here.  The  coefficient  is  19. 
Why  the  glyph  in  A9  should  stand  between  the  day  and  its  month 
glyph  is  unknown;  this  case  constitutes  one  of  the  many  unsolved 
problems  in  the  study  of  the  Maya  glyphs.  This  whole  Initial  Series 
reads  1.18.5.3.6  13  Cimi  19  Ceh. 

The  student  will  note  that  this  Initial  Series  records  a  date  14  days 
earlier  than  the  preceding  Initial  Series  (pi.  12,  A).  That  two  dates 
should  be  recorded  which  were  within  14  days  of  each  other,  and  yet 
were  more  than  3,000  years  earlier  than  practically  all  other  Maya 
dates,  is  a  puzzling  problem.  These  two  Initial  Series  from  the 
Temple  of  the  Sun  and  that  of  the  Foliated  Cross  at  Palenque,  together 
with  a  Secondary-series  date  from  the  Temple  of  the  Cross  in  the 
same  city,  have  been  thoroughly  reviewed  by  Mr.  Bowditch  (1906). 
The  conclusions  he  reaches  and  the  explanation  he  offers  to  account 
for  the  occurrence  of  three  dates  so  remote  as  these  are  very  reason- 
able, and,  the  writer  believes,  will  be  generally  accepted  by  Maya 
students. 


MORLBT]         INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  183 

In  figure  69,  A,  is  shown  the  Initial  Series  inscribed  on  the  rises 
and  treads  of  the  stairway  leading  to  House  C  in  the  Palace  at 
Palenque.^  The  introducing  glyph  is  recorded  in  Al,  and  the  Initial- 
series  number  follows  in  B1-B3.  The  student  will  readily  recognize 
the  period  glyphs  in  Bib,  A2b,  B2b,  A3b,  and  B3b.  The  head 
expressing  the  cycle  coefiicient  in  Bla  has  for  its  essential  element 
the  dots  centering  around  the  corner  of  the  mouth.  As  explained  on 
page  100,  this  characterizes  the  head  for  9  (see  fig.  52,  g-l,  where  vari- 
ants for  the  9  head  are  figured) .    In  Bl,  therefore,  we  have  recorded  9 


A  B 

FlGT.  69.   Initial  Series  showing  head- variant  numerals  and  period  glyphs:  A,  House  C  of  the  Palace 
Group  at  Palenque;  B,  Stela  P  at  Copan. 


cycles,  the  number  almost  always  found  in  Initial  Series  as  the  cycle 
coefficient.  The  essential  element  of  the  katun  coefficient  in  A2a  is 
the  forehead  ornament  composed  of  a  single  part.  This  denotes  the 
head  for  8  (see  p.  100,  and  fig.  52,  a-f;  also  compare  A2a  with  the  heads 
denoting  18  in  the  two  preceding  examples,  pi.  12,  A,  A4,  and  pi.  12, 
B,  A4,  each  of  which  shows  the  same  forehead  ornament) .  The  tun 
coefficient  in  B2a  is  exactly  like  the  cycle  coefficient  just  above 
it  in  Bla;  that  is,  9,  having  the  same  dotting  of  the  face  near  the 
corner  of  the  mouth.  The  uinal  coefficient  in  A3  a  is  13.  Com- 
pare this  head  numeral  with  A8,  plate  12,  B,  which  also  denotes  13, 
and  also  with  figure  52,  x-h' .    The  essential  elements  (see  p.  101) 


I  For  the  full  text  of  this  inscription,  see  Maudslay,  1889-1902:  iv,  pi.  23. 


184 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


are  the  large  pendulous  nose  surmounted  by  a  curl,  the  bulging  eye, 
and  the  mouth  fang,  the  last  mentioned  not  appearing  in  this  case. 
Since  the  kin  coefficient  in  B3a  is  somewhat  effaced,  let  us  call  it  0 
for  the  present^  and  proceed  to  reduce  our  number  9.8.9.13.0  to  units 
of  the  first  order  by  means  of  Table  XIII : 


Deducting  from  this  number  all  the  Calendar  Rounds  possible,  71 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and  141, 
respectively)  to  the  remainder,  we  reach  as  the  terminal  date  8  Ah  an 
13  Pop.  Now  let  us  examine  the  text  and  see  what  is  the  terminal 
date  actually  recorded.  In  A4b  the  student  will  have  little  difficulty 
in  recognizing  the  profile  variant  of  the  day  sign  Ahau  (see  fig.  16, 
V ,  i').  This  at  once  gives  us  the  missing  value  for  the  kin  coefficient 
in  B3,  for  the  day  Ahau  can  never  be  reached  in  an  Initial  Series  if 
the  kin  coefficient  is  other  than  0.  Similarly,  the  day  Imix  can  never 
be  reached  in  Initial  Series  if  the  kin  coefficient  is  other  than  1,  etc. 
Every  one  of  the  20  possible  kin  coefficients,  0  to  19,  has  a  corre- 
sponding day  to  which  it  will  always  lead,  that  is,  Ahau  to  Cauac, 
respectively  (see  Table  I).  Thus,  if  the  kin  coefficient  in  an  Initial- 
series  number  were  5,  for  example,  the  day  sign  of  the  resulting 
terminal  date  must  be  Chicchan,  since  Chicchan  is  the  fifth  name  after 
Ahau  in  Table  I.  Thus  the  day  sign  in  Initial-series  terminal  dates 
may  be  determined  by  inspection  of  the  kin  coefficient  as  well  as  by 
rule  2  (p.  140),  though,  as  the  student  will  see,  both  are  applications 
of  the  same  principle,  that  is,  deducting  all  of  the  20s  possible  and 
counting  forward  only  the  remainder.  Returning  to  our  text,  we 
can  now  say  without  hesitation  that  our  number  is  9.8.9.13.0  and 
that  the  day  sign  in  A4b  is  Ahau.  The  day  coefficient  in  A4a  is  just 
like  the  katun  coefficient  in  A2a,  having  the  same  determining  char- 
acteristic, namely,  the  forehead  ornament  composed  of  one  part.  A 
comparison  of  this  ornament  with  the  ornament  on  the  head  for  8 
in  A2a  will  show  that  the  two  forms  are  identical.  The  bifurcate 
ornament  surmounting  the  head  in  A4a  is  a  part  of  the  headdress, 
and  as  such  should  not  be  confused  with  the  forehead  ornament. 
The  failure  to  recognize  this  point  might  cause  the  student  to  identify 

1  It  is  clear  that  if  all  the  period  coefficients  above  the  kin  have  been  correctly  identified,  even  though 
the  kin  coefficient  is  unknown,  by  designating  it  0  the  date  reached  will  be  within  19  days  of  the  date 
origiaally  recorded.  Even  though  its  maximum  value  (19)  had  originally  been  recorded  here,  it  could 
have  carried  the  count  only  19  days  further.  By  using  0  as  the  kin  coefficient,  therefore,  we  can  not  be 
more  than  19  days  from  the  original  date. 


Bl=  9X144,000 
A2=  8X  7,200 
B2=  9X  360 
A3  =  13X  20 
B3=  OX  1 


1,  296,  000 
57,  600 
3,  240 
260 
0 


1,  357,  100 


MORLEY]      INTRODUCTION  TO  .STUDY  OP  MAYA  HIEROGLYPHS  185 

A4a  as  the  head  for  1,  that  is,  having  a  forehead  ornament  composed 
of  more  than  one  part,  instead  of  the  head  for  8.  The  month  %ph 
which  follows  in  B4b,  is  unfortmiately  effaced,  though  its  coefficient 
m  B4a  is  clearly  the  head  for  13.  Compare  B4a  with  the  uinal  coeffi- 
cient m  A3a  and  with  the  heads  for  13  in  figure  52,  x-V .  As  recorded 
therefore,  the  termma.1  date  reads  8  Ahau  13  ?,  thus  agreeing  in  every 
particular  so  far  as  it  goes  with  the  termmal  date  reached  Iby  calcu- 
lation, 8  Ahau  13  Pop.  In  all  probability  the  effaced  sign  in  B4b  oricri- 
nally  was  the  month  Pop.  The  whole  Initial  Series  therefore  reads 
9.8.9.13.0  8  Ahau  13  Pop. 

In  figure  69,  B,  is  shown  the  Initial  Series  from  Stela  P  at  Copan  ' 
The  introducing  glyph  appears  in  A1-B2  and  is  followed  bv  the  Initial- 
series  number  in  A3-B4.  The  student  will  readily  identify  A3,  B3, 
and  A4  as  9  cycles,  9  katuns,  and  10  tuns,  respectively.  Note  the 
beard  on  the  head  representing  the  number  9  in  both  A3a  and  B3a.. 
As  explained  on  page  100,  this  characteristic  of  the  head  for  9  is  not 
always  present  (see  fig.  52,  g-i) .  The  uinal  and  kin  glyphs  have  been 
crowded  together  into  one  glyph-block,  B4,  the  uinal  appearing  in 
B4a  and  the  km  in  B4b.  Both  their  coefficients  are  0,  which  is 
expressed  in  each  case  by  the  form  shown  in  figure  47.  The  whole 
number  recorded  is  9.9.10.0.0;  reducing  this  to  units  of  the  first  order 
by  means  of  Table  XIII,  we  obtain: 

A3  =  9X144,000  =  1,296,000 
B3  =  9X  7,200=  64,800 
A4  =10X  360=  3,600 
B4a=  Ox  20=  0 
B4b=  Ox  1=  0 


1,  364,  400 

Deducting  from  this  number  all  of  the  Calendar  Rounds  possible,  71 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and  141, 
respectively)  to  the  remainder,  the  terminal  date  reached  will  be 
2  Ahau  13  Pop.  In  A5a  the  day  2  Ahau  is  very  clearly  recorded,  the 
day  sign  being  expressed  by  the  profile  variant  and  the  2  by 'two 
dots  (incorrectly  shown  as  one  dot  in  the  accompanying  drawing^^ 
Passing  over  A5b,  B5,  and  A6  we  reach  in  B6a  the  closing  glyph  of 
the  Supplementary  Series,  and  in  the  follomng  glyph,  B6b,  the 
month  part  of  this  terminal  date.  The  coefficient  is  13,  and  compar- 
ing the  sign  itself  with  the  month  signs  in  figure  19,  it  will  be  seen  that 
the  form  in  a  (Pop)  is  the  month  recorded  here.  The  whole  Initial 
Series  therefore  reads  9.9.10.0.0  2  Ahau  13  Pop. 

1  For  the  full  text  of  this  inscription  see  Maudslay,  1889-1902:  r,  pis.  88,  89 

2  While  at  Copan  the  writer  made  a  personal  examination  of  this  monuiient  and  found  that  Mr  Mauds- 
lay's  drawmg  is  mcorrect  as  regards  the  coefficient  of  the  day  sign.  The  original  has  two  numerical  dots 
between  two  crescents,  whereas  the  Maudslay  drawing  shows  one  numerical  dot  between  two  distinct 
pairs  of  crescents,  each  pair,  however,  of  different  shape. 


186 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


In  figure  70  is  illustrated  the  Initial  Series  from  Zoomorph  G  at 
Quirigua.^    The  introducing  glyph  appears  in  A1-B2  and  is  followed 
in  Cl-Hl  by  the  Initial-series  number.    Glyphs  Cl  Dl  record  9 
cycles.    The  dots  on  the  head  for  9  in  Cl  are 
partially  effaced.    In  C2  is  the  katun  coefficient 
and  in  D2  the  katun  sign.   The  determining  char- 
acteristic of  the  head  for  7  appears  in  C2,  namely, 
the  scroll  passing  imder  the  eye  and  projecting 
i   upward  and  in  front  of  the  forehead.    See  page 
I    100  and  figure  51,  w.    It  would  seem,  then,  at 
J  first  sight  that  7  katuns  were  recorded  in  C2  D2. 

0  That  this  was  not  the  case,  however,  a  closer  ex- 
amination  of  C2  will  show.  Although  the  lower 

1  part  of  this  glyph  is  somewhat  weathered,  enough 
still  remains  to  show  that  this  head  originally  had  a 

2  fleshless  lower  j  aw,  a  character  increasing  its  value 
M  by  10.  Consequently,  instead  of  having  7  katuns 
I  in  C2  D2  we  have  17  (7  + 10)  katuns.  Compare 
I  C2  with  figure  53,  j-m.  In  El  Fl,  15  tuns  are 
a  recorded.  The  tun  headdress  in  El  gives  the  value 
S  5  to  the  head  there  depicted  (see  fig.  51,  n~s)  and 
I  the  fleshless  lower  jaw  adds  10,  making  the  value 
I  of  El  15.  Compare  figure  53,  5-6,  where  examples 
I  of  the  head  for  15  are  given.  Glyphs  E2  and  F2 
I  represent  0  uinals  and  Gl  HI  0  kins;  note  the 
I  clasped  hand  in  E2  and  Gl,  which  denotes  the  0 
^  in  each  case.  This  whole  number  therefore  reads 
I  9,17.15.0.0.  Reducing  this  to  units  of  the  first 
I  order  by  means  of  Table  XIII,  we  have: 
I  Cl  Dl=  9X144,000  =  1,296,000 
I               C2  D2  =  17X     7,200=  122,400 


El  F1  =  15X 
E2  F2=  OX 
Gl  Hl=  OX 


360  = 
20  = 
1  = 


5,400 
0 
0 


1,423,  800 

Deducting  from  this  number  all  the  Calendar 
Rounds  possible,  75  (see  Table  XVI),  and  apply- 
ing rules  1,  2,  and  3  (pp.  139,  140,  and  141,  respec- 
tively), to  the  remainder,  the  terminal  day  reached 
will  be  5  Ahau  3  Muan.  The  day  is  recorded  in  G2  112.  The  day  sign 
in  112  is  quite  clearly  the  grotesque  head  variant  for  Ahau  in  figure 
16,  — ]c\  The  presence  of  the  tun  headdress  in  G2  indicates  that  the 
coefficient  here  recorded  must  have  been  either  5  or  15,  depending 


For  the  full  text  of  this  inscription  see  Maudslay,  1889-1902:  n,  pis.  41-44. 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEKO(JLYPHS 


187 


on  whether  or  not  the  lower  part  of  the  head  origmally  had  a  flesh- 
less  lower  jaw  or  not.  In  this  particular  case  there  is  no  room  for 
doubt,  since  the  numeral  in  G2  is  a  day  coefficient,  and  day  coeffi- 
cients as  stated  in  Chapter  III,  can  never  rise  above  13.  Conse- 
quently the  number  15  can  not  be  recorded  in  G2,  and  this  form 
must  stand  for  the  number  5. 

Passing  over  II  Jl,  12  J2,  Kl  Ll,  K2  L2,  we  reach  m  Ml  the  clos- 
ing glyph  of  the  Supplementary  Series,  here  shown  with  a  coeffi- 
cient of  10,  the  head  having  a  fleshless  lower  jaw.  The  month  sign 
follows  in  Nl.  The  coefficient  is  3  and  by  comparing  the  sign  itself 
with  the  month  glyphs  in  figure  19,  it  will  be  apparent  that  the  sign 
for  Muan  in  a'orh'  is  recorded  here.  The  Initial  Series  of  this  monu- 
ment therefore  is  9.17.15.0.0  5  Ahau  3  Muan. 

In  closing  the  presentation  of  Initial-series  texts  which  show  both 
head-variant  numerals  and  period  glyphs,  the  writer  has  thought  best 
to  figure  the  Initial  Series  on  Stela  15  at  Copan,  because  it  is  not  only 
the  oldest  Initial  Series  at  Copan,  but  also  the  oldest  one  known  in 
which  head-variant  numerals  are  used  ^  (see  pi.  13).  The  introducing 
glyph  appears  at  A1-B2.  There  follows  in  A3  a  number  too  much 
effaced  to  read,  but  which,  on  the  basis  of  all  our  previous  experience, 
we  are  justified  in  calling  9.  Similarly  B3  must  be  the  head  variant 
of  the  cycle  sign.  The  numeral  4  is  clearly  recorded  in  A4.  Note 
the  square  irid,  protruding  fang,  and  mouth  curl.  Compare  A4  with 
figure  51,  j-m.  Although  the  glyph  in  B4  is  too  much  effaced  to 
read,  we  are  justified  in  assuming  that  it  is  the  head  variant  of  the 
katun  sign.  The  glyph  in  A5  is  the  numeral  10.  Note  the  fleshless 
lower  jaw  and  other  characteristics  of  the  death's-head.  Again  we 
are  justified  in  assuming  that  B5  must  be  the  head  variant  of  the  tun 
sign.  The  glyphs  A6,  B6  clearly  record  0  uinals.  Note  the  clasped 
hand  denoting  zero  in  A6,  and  the  curling  mouth  fang  of  the  uinal 
period  glyph  in  B6.  This  latter  glyph  is  the  full-figure  form  of  the 
uinal  sign  2  (a  frog).  Compare  B6  with  figure  33,  which  shows  the 
uinal  sign  on  Stela  D  at  Copan.  The  stela  is  broken  ofi;  just  below 
the  uinal  sign  and  its  coefficient;  and  therefore  the  kin  coefficient 
and  sign,  the  day  coefficient  and  sign,  and  the  month  coefficient  and 
sign,  are  missing.  Assembling  the  four  periods  present,  we  have 
9.4.10.0.?.  Calling  the  missing  kin  coefficient  0,  and  reducing  this 
number  to  units  of  the  first  order  by  means  of  Table  XIII,  we  have: 

A3B3=  9X144,000  =  1,296,000 

A4B4=  4x     7,200=  28,800 

A5B5  =  10X        360=  3,600 

A6  B6  =  0  X         20  =  0 

OX  1=  0  - 


1,328,400 


1  For  the  text  of  this  monument  see  Spinden,  1913:  VT,  pi.  23,  2. 

2  For  the  discussion  of  full-figure  glyphs,  see  pp.  65-73. 


188 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


Deducting  from  this  number  all  the  Calendar  Rounds  possible,  69 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and  141, 
respectively)  to  the  remainder,  the  terminal  date  reached  wiU  be 
12  Ahau  8  Mol.  This  date  is  reached  on  the  assumption  that  the  miss- 
ing kin  coefficient  was  zero.  This  is  a  fairly  safe  assumption,  since 
when  the  tun  coefficient  is  either  0,  5,  10,  or  15  (as  here)  and  the  uinal 
coefficient  is  0  (as  here),  the  kin  coefficient  is  almost  invariably  zero. 
That  is,  the  close  of  an  even  ho  tun  in  the  Long  Count  is  recorded. 

While  at  Copan  in  May,  1912,  the  writer  was  shown  a  fragment  of 
a  stela  which  he  was  told  was  a  part  of  this  monument  (Stela  15). 
This  showed  the  top  parts  of  two  consecutive  glyphs,  the  first  of 
which  very  clearly  had  a  coefficient  of  12  and  the  one  following  of  8. 
The  glyphs  to  which  these  coefficients  belonged  were  missing,  but  the 
coincidence  of  the  two  numbers  12  ( ?)  8  ( ?)  was  so  striking  when  taken 
into  con^ideration  with  the  fact  that  these  were  the  day  and  month 
coefficients  reached  by  calculation,  that  the  writer  was  inclined  to 
accept  this  fragment  as  the  missing  part  of  Stela  15  which  showed 
the  terminal  date.  This  whole  Initial  Series  therefore  reads :  9.4.10.0.0 
12  Ahau  8  Mol.  It  is  chiefly  interesting  because  it  shows  the  earliest 
use  of  head-variant  numerals  known. 

In  the  foregoing  texts  plate  12,  A,  B,  figure  69,  A,  B,  and  figure  70, 
the  head-variant  numerals  0, 1,  3,  4,  5,  6,  8,  9,  10,  13,  14, 15,  17,  and  18 
have  been  given,  and,  excepting  the  forms  for  2,  11,  and  12,  these 
include  examples  of  all  the  head  numerals.^  No  more  texts  specially 
illustrating  this  type  of  numeral  will  be  presented,  but  when  any  of 
the  head  numerals  not  figured  above  (2,  7,  11,  12,  16,  and  19) 
occur  in  future  texts  their  presence  wiU  be  noted. 

Before  taking  up  the  consideration  of  unusual  or  irregular  Initial 
Series  the  writer  has  thought  best  to  figure  one  Initial  Series  the 
period  glyphs  and  numerals  of  which  are  expressed  by  full-figure 
forms.  As  mentioned  on  page  68,  such  inscriptions  are  exceedingly 
rare,  and  such  glyphs,  moreover,  are  essentially  the  same  as  head- 
variant  forms,  since  their  determining  characteristics  are  restricted 
to  their  head  parts,  which  are  exactly  like  the  corresponding  head- 
variant  forms.  This  fact  will  greatly  aid  the  student  in  identifying 
the  full-figure  glyphs  in  the  following  text. 

In  plate  14  is  figured  the  Initial  Series  from  Stela  D  at  Copan.^ 
The  introducing  glyph  is  recorded  in  Al.  The  variable  central 
element  in  keeping  with  the  other  glyphs  of  the  inscription  appears 
here  as  a  fuU  figure,  the  lower  part  of  which  is  concealed  by  the  tun- 
sign.^ 

1  The  characteristics  of  the  heads  for  7,  14, 16,  and  19  will  be  found  in  the  heads  for  17, 4,  6,  and  9,  respec- 
.tively. 

2  For  the  full  text  of  this  inscription  see  Maudslay,  1889-1902:  i,  pis.  47,  48. 

3  The  student  will  note  also  in  "connection  with  this  glyph  that  the  pair  of  comblike  appendages  usually 
found  are  here  replaced  by  a  pair  of  fishes.  As  explained  on  pp.  65-66,  the  fish  represents  probably  the 
original  form  from  which  the  comblike  element  was  derived  in  the  process  of  glyph  conventionalization. 
The  full  original  form  of  this  element  is  therefore  in  keeping  with  the  other  full-figure  forms  in  this  text. 


MOBLET]      INTRODUCTION'  TO  STUDY  OF  MAYA  HIEROGLYPHS  189 

The  Initial-series  number  itself  appears  in  B1-B3.  The  cycle  sign 
is  a  grotesque  bird,  designated  by  Mr.  Bowditch  a  parrot,  an  identifi- 
cation which  the  hooked  beak  and  claws  strongly  suggest.  The 
essential  element  of  the  cycle  sign,  however,  the  clasped  hand,  appears 
only  in  the  head  of  this  bird,  where  the  student  will  readily  find  it. 
Indeed,  the  head  of  this  full-figure  form  is  nothing  more  nor  less  than 
a  head-variant  cycle  glyph,  and  as  such  determines  the  meaning  of 
the  whole  figure.  Compare  this  head  with  figure  25,  d-f,  or  with  any  ' 
of  the  other  head-variant  cycle  forms  figured  in  the  preceding  texts. 
This  grotesque  ''cyble  bird,"  perhaps  the  parrot,  is  bound  to  the  back 
of  an  anthropomorphic  figure,  which  we  have  every  reason  to  suppose 
records  the  cycle  coefiicient.  An  examination  of  this  figure  will  show 
that  it  has  not  only  the  dots  on  the  lower  part  of  the  cheek,  but  also 
the  beard,  both  of  which  are  distinctive  features  of  the  head  for  9. 
Compare  this  head  with  figure  52,  g-l^  or  with  any  other  head  variants 
for  the  numeral  9  already  figured.  Bearing  in  mind  that  the  heads 
only  present  the  determining  characteristics  of  fuU-figure  glyphs,  the 
student  wiU  easily  identify  Bl  as  recording  9  cycles. 

The  katun  and  its  coefiicient  are  represented  in  A2,  the  former  by 
a  grotesque  bird,  an  eagle  according  to  Mr.  Bowditch,  and  the  latter 
by  another  anthropomorphic  figure.  The  period  glyph  shows  no 
essential  element  recognizable  as  such,  and  its  identification  as  the 
katun  sign  therefore  rests  on  its  position,  immediately  following  the 
cycle  sign.  The  head  of  the  full  figure,  which  represents  the  katun 
coefiicient,  shows  the  essential  clement  of  the  head  for  5,  the  tun 
headdress.  It  has  also  the  fleshless  lower  jaw  of  the  head  for  10. 
The  combination  of  these  two  elements  in  one  head,  as  we  have  seen, 
indicates  the  numeral  15,  and  A2  therefore  records  15  katuns.  Com- 
pare the  head  of  this  anthropomorphic  figure  with  figure  53,  h-e. 

The  tun  and  its  coefficient  are  represented  in  B2.  The  former 
again  appears  as  a  grotesque  bird,  though  in  this  case  of  undeter- 
mined nature.  Its  head,  however,  very  clearly  shows  the  essential 
element  of  the  head-variant  tun  sign,  the  fieshless  lower  jaw.  Com- 
pare this  form  with  figure  29,  e-g,  and  the  other  head-variant  tun 
signs  already  illustrated.  The  head  of  the  anthropomorphic  figure, 
which  denotes  the  tun  coefficient,  is  just  like  the  head  of  the  anthro- 
pomorphic figure  in  the  preceding  glyph  (A2),  except  that  in  B2  the 
head  has  no  fleshless  lower  jaw. 

Since  the  head  in  A2  with  the  fleshless  lower  jaw  and  the  tun 
headdress  represents  the  numeral  15,  the  head  in  B2  without  the 
former  but  with  the  latter  represents  the  numeral  5.  Compare  the 
head  of  the  anthropomorphic  figure  in  B2  with  figure  51,  n-s.  It  is 
clear,  therefore,  that  5  tuns  are  recorded  in  B2. 

The  uinal  and  its  coefficient  in  A3  are  equally  clear.  The  period 
glyph  here  appears  as  a  frog  (Maya,  ^to),  which,  as  we  have  seen  else- 


190 


BUKEAU  OF  AMEEICAN  ETHNOLOGY 


[BULL.  57 


"where,  may  have  been  chosen  to  represent  the  20-day  period  because 
of  the  similarity  of  its  name,  uo,  to  the  name  of  this  period,  u,  or 
uinal.  The  head  of  the  anthropomorphic  figure  which  clasps  the 
frog's  foreleg  is  the  head  variant  for  0.  Note  the  clasped  hand  across 
the  lower  part  of  the  face,  and  compare  this  form  with  figure  53, 
s^.    The  whole  glyph,  therefore,  stands  for  0  uinals. 

In  B3  are  recorded  the  kin  and  its  coefficient.  The  period  glyph 
*  here  is  represented  by  an  anthropomorphic  figure  with  a  grotesque 
head.  Its  identity,  as  representing  the  kins  of  this  number,  is  better 
established  from  its  position  in  the  number  than  from  its  appearance, 
which  is  somewhat  irregular.  The  kin  coefficient  is  just  like  the  uinal 
coefficient — an  anthropomorphic  figure  the  head  of  which  has  the 
clasped  hand  as  its  determining  characteristic.  Therefore  B3  records 
0  kins. 

The  whole  number  expressed  by  B1-B3  is  9.15.5.0.0;  reducing  this 
by  means  of  Table  XIII  to  units  of  the  first  order^  we  have: 
Bl=  9X144,000  =  1,296,000 
A2  =  15X  7,200=  108,000 
B2=  5X  360=  1,800 
A3=  OX  20=  0 
B3=  Ox  1=  0 

1,  405,  800 

Deducting  from  this  number  all  the  Calendar  Eounds  possible,  74 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and 
141  respectively),  to  the  remainder,  the  terminal  date  reached  will 
be  10  Aliau  8  Chen. 

The  day  part  of  this  terminal  date  is  recorded  in  A4.  The  day  sign 
Ahau  is  represented  as  an  anthropomorphic  figure,  crouching  within 
the  customary  day-sign  cartouche.  The  head  of  this  figure  is  the 
familiar  profile  variant  for  the  day  sign  Ahau,  seen  in  figure  16, 
i' ,  This  cartouche  is  clasped  by  the  left  arm  of  another  anthropo- 
morphic figure,  the  day  coefficient,  the  head  of  which  is  the  skull, 
denotiag  the  numeral  10.  Note  the  ffeshless  lower  jaw  of  this  head 
and  compare  it  with  the  same  element  in  figure  52,  m-r.  This  glyph 
A4  records,  therefore,  the  day  reached  by  the  Initial  Series,  10  Ahau. 

The  position  of  the  month  glyph  ia  this  text  is  most  unusual. 
Passing  over  B4,  the  first  glyph  of  the  Supplementary  Series,  the 
month  glyph  follows  it  immediately  in  A5.  The  month  coefficient 
appears  again  as  an  anthropomorphic  figure,  the  head  of  which  has 
for  its  determining  characteristic  the  forehead  ornament  composed 
of  one  part,  denoting  the  numeral  8.  Compare  this  head  with  the 
heads  for  8,  in  figure  52,  a-f.  The  month  sign  itself  appears  as  a  large 
grotesque  head,  the  details  of  which  present  the  essential  elements 
of  the  month  here  recorded — Chen.    Compare  with  figure  19,  o,  p. 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57    PLATE  15 


/  I 


A 


A.    THE  INSCRIPTION  ARRANGED  ACCORDING     B.    KEY  TO  SEQUENCE  OF  GLYPHS  IN  A 
TO  A  MAT  PATTERN 

INITIAL  SERIES  ON   STELA  J,  COPAN 


MORLEY]      INTEODUCTIOIT  TO  STUDY  OF  MAYA  HIEEOGLYPHS  191 


The  superfix  of  figure  16,  o,  p,  has  been  retained  unchanged  as  the 
superfix  in  A5b.  The  element  (*)  appears  just  ahove  the  eye 
of  the  grotesque  head,  and  the  element  (**)  on  the  left-hand  ^ 
side  about  where  the  ear  lobe  should  be.  The  whole  glyph  *  ** 
unmistakably  records  a  head  variant  of  the  month  glyph  Chen,  and 
this  Initial  Series  therefore  reads  9.15.5.0.0  10  Ahau  8  Chen. 

The  student  will  note  that  this  Initial  Series  records  a  date  just 
5  tuns  later  than  the  Initial  Series  on  Stela  B  at  Copan  (pi.  7,  A). 
According  to  the  writer's  opinion,  therefore.  Stelae  B  and  D  marked 
two  successive  hotuns  at  this  city. 

We  come  now  to  the  consideration  of  Initial  Series  which  are  either 
imusual  or  irregular  in  some  respect,  examples  of  which  it  is  necessary 
to  give  in  order  to  familiarize  the  student  with  all  kinds  of  texts. 

The  Initial  Series  in  plate  15,  A,^  is  figured  because  of  the  very 
unusual  order  followed  by  its  glyphs.  The  sequence  in  which  these 
succeed  each  other  is  given  in  B  of  that  plate.  The  scheme  followed 
seems  to  have  been  that  of  a  mat  pattern.  The  introducing 
glyph  appears  in  position  0  (pi.  15,  B),  and  the  student  will  readily 
recognize  it  in  the  same  position  in  A  of  the  same  plate.  The 
Initial  Series  number  follows  in  1,  2,  3,  4,  and  5  (pi.  15,  B).  Kefer- 
ring  to  these  corresponding  positions  in  A,  we  find  that  9  cycles  are 
recorded  in  1,  and  13  katuns  in  2.  At  this  point  the  diagonal  glyph- 
band  passes  under  another  band,  emerging  at  3,  where  the  tun  sign 
with  a  coefficient  of  10  is  recorded.  Here  the  band  turns  again  and, 
crossing  backward  diagonally,  shows  0  uinals  in  4.  At  this  point  the 
band  passes  under  three  diagonals  running  in  the  opposite  direction, 
emerging  g,t  position  5,  the  glyph  in  which  are  recorded  0  kins. 

This  number  9.13.10,0.0  reduces  by  means  of  Table  XIII  to  units 
of  the  first  order,  as  follows : 

1=  9X144,000  =  1,296,000 

2  =  13X     7,200-  93,600 

3  =  10X-  360=  3,600 
4=  OX  20=  0 
5=  OX  1=  0 


1,  393,  200 


Deducting  from  this  number  all  the  Calendar  Rounds  possible,  73 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and  141, 
respectively)  to  the  remainder,  the  terminal  date  reached  will  be 
7  Ahau  3  Cumhu.  Referring  again  to  plate  15,  ^,  for  the  sequence  of 
the  glyphs  in  this  text,  it  is  clear  that  the  day  of  this  terminal  date 
should  be  recorded  in  6,  immediately  after  the  kins  of  the  Initial- 
series  number  in  6.    It  will  be  seen,  however,  in  plate  15,  A,  that 

1  For  the  full  text  of  this  inscription,  see  Maudslay,  1889-1902:  i,  pis.  66-71. 


192 


BUREAU  OF  AMEEICAN  ETHNOLOGY 


[bull.  57 


^lyph  6  is  effaced,  and  consequently  the  day  is  missing.  Passing  over 
7,  8,  9,  10,  and  11,  in  A  and  B  of  the  plate  named,  we  reach  in  the 
lower  half  of  12  the  closing  glyph  of  the  Supplementary  Series  here 
shown  with  a  coefficient  of  10.  Compare  this  form  with  figure  65. 
The  month  glyph,  therefore,  should  follow  in  the  upper  half  of  13.^ 
This  glyph  is  very  clearly  the  form  for  the  month  Cumhu  (see  fig.  19,  g', 
V),  and  it  seems  to  have  attached  to  it  the  bar  and  dot  coefficient  8. 
A  comparison  of  this  with  the  month  coefficient  3,  determined  above 
by  calculation,  shows  that  the  two  do  not  agree,  and  that  the  month 
coefficient  as  recorded  exceeds  the  month  coefficient  determined  by 
calculation,  by  5,  or  in  Maya  notation,  1  bar.  Since  the  Initial-series 
number  is  very  clearly  9.13.10.0.0,  and  since  this  number  leads  to  the 
terminal  date  7  Ahau  3  Cumhu,  it  would  seem  that  the  ancient  scribes 
had  made  an  error  in  this  text,  recording  1  bar  and  3  dots  instead  of 
3  dots  alone.  The  writer  is  inclined  to  believe,  however,  that  the  bar 
here  is  only  ornamental  and  has  no  numerical  value  whatsoever,  hav- 
ing been  inserted  solely  to  balance  this  glyph.  If  it  had  been  omitted, 
the  month  sign  would  have  had  to  be  greatly  elongated  and  its  pro- 
portions distorted  in  order  to  fill  completely  the  space  available. 
According  to  the  writer's  interpretation,  this  Initial  Series  reads 
9.13.10.0.0  7  Ahau  3  Cumhu. 

The  opposite  face  of  the  above-mentioned  monument  presents  the 
same  interlacing  scheme,  though  in  this  case  the  glyph  bands  cross  at 
right  angles  to  each  other  instead  of  diagonally. 

The  only  other  inscription  in  the  whole  Maya  territory,  so  far  as 
the  writer  knows,  which  at  all  parallels  the  curious  interlacing  pattern 
of  the  glyphs  on  the  back  of  Stela  J  at  Copan,  just  described,  is  Stela  H 
at  Quirigua,  illustrated  in  figure  71.^  The  drawing  of  this  inscription 
appears  in  a  of  this  figure  and  the  key  to  the  sequence  of  the  glyphs  in  h. 
The  introducing  glyph  occupies  position  1  and  is  followed  by  the 
Initial  Series  in  2-6.  The  student  will  have  little  difficulty  in  iden- 
tifying 2,  3,  and  4  as  9  cycles,  16  katims,  and  0  tuns,  respectively. 
The  uinal  and  kin  glyphs  in  5  and  6,  respectively,  are  so  far  effaced 
that  in  order  to  determine  the  values  of  their  coefficients  we  shaU 
have  to  rely  to  a  large  extent  on  other  inscriptions  here  at  Quirigua. 
For  example,  every  monument  at  Quirigua  which  presents  an  Initial 
Series  marks  the  close  of  some  particular  ho  tun  in  the  Long  Count; 
consequently,  all  the  Initial  Series  at  Quirigua  which  record  these 
hotun  endings  have  0  for  their  uinal  and  kin  coefficients.^    This  abso- 

1  The  student  should  remember  that  in  this  diagonal  the  direction  of  reading  is  from  bottom  to  top. 
See  pi.  15,  B,  glyphs  7,  8,  9,  10,  11,  12,  etc.  Consequently  the  upper  half  of  13  follows  the  lower  half  in 
this  particular  glyph. 

2  For  the  full  text  of  this  inscription  see  Hewett,  1911:  pi.  xxn  B. 

3  A  few  monuments  at  Quirigua,  namely,  Stelae  F,  D,  E,  and  A,  have  two  Initial  Series  each.  In  A  both 
of  the  Initial  Series  have  0  for  the  coefficients  of  their  uinal  and  kin  glyphs,  and  in  F,  D,  E,  the  Initial 
Series  which  shows  the  position  of  the  monument  in  the  Long  Count,  that  is,  the  Initial  Series  showing 
the  hotun  ending  which  it  marks,  has  0  for  its  uinal  and  kin  coefficients. 


MOELBY]      IITTKODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


193 


lute  uniformity  in  regard  to  the  uinal  and  kin  coefficients  in  all  the 
other  Initial  Series  at  Quirigua  justifies  the  assumption  that  in  the 
text  here  under  discussion  0  uinals  and  0  kins  were  originally  recorded 
in  glyphs  5  and  6,  respec- 
tively. Furthermore,  an 
inspection  of  the  coeffi- 
cients of  these  two  glyphs 
in  figure  71,  a,  shows  that 
both  of  them  are  of  the 
same  general  size  and 
shape  as  the  tun  coeffi- 
cient in  4,  which,  as  we 
have  seen,  is  very  clearly  0. 
It  is  more  than  probable 
that  the  uinal  and  kin  co- 
efficients in  this  text  were 
originally  0,  like  the  tun  co- 
efficient, and  that  through 
Weathering  they  have  been 
eroded  down  to  their  pres- 
ent shape.  In  figure  72,  a,  is  shown  the  tun  coefficient  and  beside  it 
in  h,  the  uinal  or  kin  coefficient.  The  dotted  parts  in  h  are  the  lines 
which  have  disappeared  through  erosion,  if  this  coefficient  was  origi- 
nally 0.  It  seems  more  than  likely  from  the  foregoing  that  the  uinal 
and  kin  coefficients  in  this  number  were  originally  0,  and  proceeding 
on  this  assumption,  we  have  recorded  in  glyphs  2-6,  figure  71,  a,  the 
number  9.16.0.0.0. 

Keducing  this  to  units  of  the  first  order  by  means  of  Table  XIII, 
we  have: 

5=  9X144,000  =  1,296,000 
6  =  16X  7,200==  115,200 
7=  OX  360=  0 
8=  OX  20=  0 

9=  OX  1=  0 


Fig.  71.   Initial  Series  on  Stela  H,  Quirigua:  a,  Mat  pattern 
of  glypli  sequence;  &,  key  to  sequence  of  glyphs  in  a. 


1,411,200 


Deducting  from  this  number  all  the  Calendar  Rounds  possible,  74 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and 
141,  respectively)  to  the  remainder,  the  terminal  date  2  Ahau  13 
Tzec  will  be  reached. 

In  spite  of  some  weathering,  the  day  part  of  the  terminal  date 
appears  in  glyph  7  immediately  after  the  kin  glyph  in  6.  The  coeffi- 
cient, though  somewhat  eroded,  appears  quite  clearly  as  2  (2  dots 
separated  by  an  ornamental  crescent).  The  day  sign  itself  is  the 
profile  variant  for  Ahau  shown  in  figure  16,7i',i\  The  agreement  of 
43508°— Bull.  57—15  ^13 


194 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


the  day  recorded  with,  the  day  determined  by  calculations  based  on 
the  assumption  that  the  kin  and  uinal  coefficients  are  both  0,  of  itself 
tends  to  establish  the  accuracy  . of  these  assimiptions.  Passing  over 
8,  9,  10,  11,  12,  13,  and  14,  we  reach  in  15  the  closing  glyph  of  the 
Supplementary  Series,  and  in  16  probably  the  month  glyph.  This 
form,  although  badly  eroded,  presents  no  features  either  in  the  outline 
of  its  coefficient  or  in  the  sign  itself  'which  would  prevent  it  repre- 
senting the  month  part  13  Tzec.  The  coefficient  is  just  wide  enough 
for  three  vertical  divisions  (2  bars  and  3  dots),  and  the  month  glyph 
itself  is  divided  into  two  parts,  a  superfix  comprising  about  one-third 
of  the  glyph  and  the  main  element  the  remaining  two-thirds.  Com- 
pare this  form  with  the  sign  for  Tzec  in  figure  19,  g,  h.  Although 
this  text  is  too  much  weathered  to  permit  ab- 
solute certainty  with  reference  to  the  reading  of 
this  Initial  Series,  the  writer  nevertheless  be- 
Heves  that  in  all  probability  it  records  the  date 
given  above,  namely,  9.16.0.0.0  2  Ahau  13  Tzec. 
If  this  is  so.  Stela  H  is  the  earliest  ho  tun-marker 
a  6  at  Quirigua.i 

FIG.  72.  The  tun,  tunai,  and  The  studcut  Will  havc  uoticcd  from  the  fore- 
kin  coefficients  on  Stela  H,  going  tcxts,  and  it  has  also  been  stated  several 
^'^iSsted^estraSo^^^^  times,  that  the  cycle  coefficient  is  almost  invari- 
theuinai  and  kin  coefficients  ably  9.  Indeed,  the  ouly  two  exceptions  to  this 
like  the  tun  coefficient.  ^-^^  inscriptions  already  figured  are  the 

Initial  Series  from  the  Temples  of  the  FoUated  Cross  and  the  Sun  at 
Palenque  (pi.  12,  A  and  B,  respectively),  in  which  the  cycle  coeffi- 
cient in  each  case  was  1.  As  explained  on  page  179,  footnote  1,  these 
two  Initial  Series  refer  probably  to  mythological  events,  and  the  dates 
which  they  record  were  not  contemporaneous  with  the  erection  of  the 
temples  on  whose  walls  they  are  inscribed;  and,  finally.  Cycle  9 
was  the  first  historic  period  of  the  Maya  civilization,  the  epoch 
which  witnessed  the  rise  and  fall  of  all  the  southern  cities. 

As  explained  on  page  179,  footnote  2,  however,  there  are  one  or  two 
Initial  Series  which  can  hardly  be  considered  as  referring  to  mytho- 
logical events,  even  though  the  dates  which  they  record  fall  in  a  cycle 
earlier  than  Cycle  9.  It  was  stated,  further,  in  the  same  place  that 
these  two  Initial  Series  were  not  f oimd  inscribed  on  large  monuments 
but  on  smaller  antiquities,  one  of  them  being  a  small  nephrite  figure 
which  has  been  designated  the  Tuxtla  Statuette,  and  the  other  a 
nephrite  plate,  designated  the  Ley  den  Plate;  and,  finally,  that  the 
dates  recorded  on  these  two  antiquities  probably  designated  contem- 
poraneous events  in  the  historic  period  of  the  Maya  civilization. 

1  In  1913  Mr.  M.  D.  Landry,  superintendent  of  the  Quirigua  district,  Guatemala  division  of  the  United 
Fruit  Co.,  found  a  still  earlier  monument  about  half  a  mile  west  of  the  main  group.  This  has  been  named 
Stela  S.  It  records  the  hotun  ending  prior  to  the  one  on  Stela  H,  i.  e.,  9.15.15.0.0  9  Ahau  18  Xul 


MOELET]      IN-TKODUCTTON  TO  STUDY  OF  MAYA  HIEKOGLYPHS 


195 


These  two  minor  antiquities  have  several  points  in  common.  Both 
are  made  of  the  same  material  (nephrite)  and  both  have  their  glyphs 
incised  instead  of  carved.  More  important,  however,  than  these 
similarities  is  the  fact  that  the  Initial  Series  recorded  on  each  of  them 
has  for  its  cycle  coefficient  the  numeral  8;  in  other  words,  both  record 
dates  which  fell  in  the  cycle  immediately  preceding  that  of  the  his- 
toric period,  or  Cycle  9.    Finally,  at  least  one  of  these  two  Initial 


Fig.  73,   The  Initial  Series  on  the  Tuxtla  Statuette,  the  oldest  Initial  Series  known  (in  the  early  part  of 

Cycle  8). 

Series  (that  on  the  Leyden  Plate),  if  indeed  not  both,  records  a  date 
so  near  the  opening  of  the  historic  period,  which  we  may  assume 
occurred  about  9.0.0.0.0  8  Aliau  13  Ceh  in  round  numbers,  that  it  may 
be  considered  as  belonging  to  the  historic  period,  and  hence  con- 
stitutes the  earliest  historical  inscription  from  the  Maya  territory. 


196 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


The  Initial  Series  on  the  first  of  these  minor  antiquities,  the  Tnxtla 
Statuette,  is  shown  in  figure  73.^  The  student  will  note  at  the  outset 
one  very  important  difference  between  this  Initial  Series — if  indeed 
it  is  one,  which  some  have  doubted — and  those  already  presented- 
No  period  glyphs  appear  in  the  present  example,  and  consequently 
the  Initial-series  number  is  expressed  by  the  second  method  (p.  129), 
that  is,  numeration  by  position,  as  in  the  codices.  See  the  discussion 
of  Initial  Series  in  the  codices  in  Chapter  VI  (pp.  266-273 ) , 
Cy/^  plates  31  and  32.    This  at  once  distinguishes  the 

*  '  *        Initial  Series  on  the  Tuxtla  Statuette  from  every  other 
Initial  Series  in  the  inscriptions  now  known.  The 


j    number  is  preceded  by  a  character  which  bears  some 
general  resemblance  to  the  usual  Initial-series  intro- 


t^ro^du^^B^g  ducing  glyph.    See  figure  74.    The  most  striking  point 
iSS/seHes       similarity  is  the  trinal  superfix,  which  is  present  in 
on  the  Tux-  both  sigus.    The  student  will  have  little  difiiculty  in 
tia  statuette,     p^adiug  the  number  here  recorded  as  8  cycles,  6  katuns, 
2  tuns,  4  uinals,  and  17  kins,  that  is,  8.6.2.4.17;  reducing  this  to  units 
of  the  first  order  by  means  of  Table  XIII,  we  have: 
8X144,  000  =  1,  152,  000 
6X     7,200=  43,200 
2X        360=  720 
4X         20=  80 
17  X  1=  17 


1,  196,  017 

Solving  this  Initial-series  number  for  its  terminal  date,  it  will  be  found 
to  be  8  Caban  0  Kankin.  Returning  once  more  to  our  text  (see  fig.  73) , 
we  find  the  day  coefficient  above  reached,  8,  is  recorded  just  below 
the  17  kins  and  appears  to  be  attached  to  some  character  the  details 
of  which  are,  unfortunately,  effaced.  The  month  coefficient  0  and 
the  month  sign  Kankin  do  not  appear  in  the  accompanying  text,  at 
least  in  recognizable  form.  This  Initial  Series  would  seem  to  be, 
therefore,  8.6.2.4.17  8  Caban  0  Kankin,  of  which  the  day  sign,  month 
coefficient,  and  month  sign  are  effaced  or  unrecognizable.  In  spite 
of  its  unusual  form  and  the  absence  of  the  day  sign,  and  the  month 
coefficient  and  sign  the  writer  is  inclined  to  accept  the  above  date  as  a 
contemporaneous  Initial  Series.^ 

The  other  Initial  Series  showing  a  cycle  coefficient  8  is  on  the 
Leyden  Plate,  a  drawing  of  which  is  reproduced  in  figure  75,  A.  This 
Initial  Series  is  far  more  satisfactory  than  the  one  just  described,  and 

1  For  the  full  text  of  this  inscription  see  Holmes,  1907:  pp.  691  et  seq.,  and  pis.  34-41. 

2  For  a  full  discussion  of  the  Tuxtla  Statuette,  including  the  opinions  of  several  writers  as  to  its  inscrip- 
tion, see  Holmes,  1907:  pp.  691  et  seq.  The  present  writer  gives  therein  at  some  length  the  reasons  which 
have  led  him  to  accept  this  inscription  as  genuine  and  contemporaneous. 


MORLET]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


197 


its  authenticity,  generally  speaking,  is  unquestioned.    The  student 
will  easily  identify  A1-B2  as  an  Initial-series  introducing  glyph,  even 
though  the  pair  of  comblike 
appendages   flanking  the 
central  element  and  the 
tun  tripod  are  both  want- 
ing.   Compare  this  form 
with  figure  24 .  The  Initial- 
series  number,  expressed  by 
normal-form  numerals  and 
head-variant  period  glyphs, 
follows  in  A3-A7.  The  for- 
mer are  all  very  clear,  and 
the  number  may  be  read 
from  them  in  spite  of  cer- 
tain irregularities  in  the  cor- 
responding period  glyphs. 
For  example,  the  katun 
head  in  A4  has  the  clasped 
hand,  which  is  the  distin- 
guishing characteristic  of 
the  cycle  head,  and  as  such 
should  have  appeared  in 
the  head  in  A3.  Neither 
the  tun  head  in  A5  nor  the 
kin  head^  in  A7  shows  an 
essential  element  hereto- 
fore found  distinguishing 
these  particular  period 
glyphs.    Indeed,  the  only 
period  glyph  of  the  five 
showing  the  usual  essen- 
tial element  is  the  uinal 
head  in  A6,  where  the  large 
mouth  curl  appears  very 
clearly.    However,  the 
number  recorded  here  may 
be  read  as  8.14.3.1.12  from 
the  sequence  of  the  coeffi- 
cients— that  is,  their  posi- 
tion with  reference  to  the 
introducing  glyph — a  readmg,  moreover,  which  is  confirmed  by  the 
only  known  period  glyph,  the  uinal  sign,  standing  in  the  fourth  posi- 
tion after  the  introducing  glyph. 


Fig.  75.  Drawings  of  the  Initial  Series:  A,  On  the  Ley  den 
Plate.  This  records  a  Cycle-S  date  and  next  to  the  Tuxtla 
Statuette  Initial  Series,  is  the  earliest  known.  B,  On  a  lintel 
from  the  Temple  of  the  Initial  Series,  Chichen  Itza.  This 
records  a  Cycle-10  date,  and  is  one  of  the  latest  Initial  Series 
known. 


198 


BUREAU  OF  AMEEICAN  ETHNOLOGY 


[bull.  57 


Reducing  this  number  to  units  of  the  first  order  by  means  of  Table 
XIII,  we  have: 


A3  = 

8  X  144, 

000  =  1, 

152, 

000 

A4  = 

14  X  7, 

200  = 

100, 

800 

A5  = 

3X 

360  = 

1, 

080 

A6  = 

IX 

20  = 

20 

A7  = 

12  X 

1  = 

12 

1,253,912 

Deducting  from  this  number  all  the  Calendar  Rounds  possible,  66 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and  141, 
respectively)  to  the  remainder,  the  terminal  date  reached  will  be 
1  Eb  0  Yaxkin.  The  day  part  of  this  date  is  very  clearly  recorded 
in  A8,  the  coefficient  1  being  expressed  by  one  dot,  and  the  day  sign 
itself  having  the  hook  surrounded  by  dots,  and  the  prominent  teeth, 
both  of  which  are  characteristic  of  the  grotesque  head  which  denotes 
the  day  Eb.    See  figure  16,  s-u. 

The  month  glyph  appears  in  A9a,  the  lower  half  of  which  unmis- 
takably records  the  month  Yaxkin.  (See  fig.  19,  Ic,  I.)  Note  the  yax 
and  Mn  elements  in  each.  The  only  difficulty  here  seems  to  be  the 
fact  that  a  bar  (5)  is  attached  to  this  glyph.  The  writer  believes, 
however,  that  the  unexplained  element  (*)  is  the  month  co- 
efficient  in  this  text,  and  that  it  is  an  archaic  form  for  0.  He  * 
would  explain  the  bar  as  being  merely  ornamental.  The  whole  Initial 
Series  reads:  8.14.3.1.12  1  Eb  0  Yaxkin. 

The  fact  that  there  are  some  few  irregularities  in  this  text  confirms 
rather  than  invalidates  the  antiquity  which  has  been  ascribed  to  it 
by  the  writer.  Dating  from  the  period  when  the  Maya  were  just 
emerging  from  savagery  to  the  arts  and  practices  of  a  semicivilized 
state,  it  is  not  at  all  surprising  that  this  inscription  should  refiect 
the  crudities  and  uncertainties  of  its  time.  Indeed,  it  is  quite  possi- 
ble that  at  the  very  early  period  from  which  it  probably  dates 
(8.14.3.1.12  1  Eb  0  Yaxkin)  the  period  glyphs  had  not  yet  become 
sufficiently  conventionalized  to  show  individual  peculiarities,  and 
their  identity  may  have  been  determuied  solely  by  their  position 
with  reference  to  the  introducmg  glyph,  as  seemingly  is  the  case  in 
some  of  the  period  glyphs  of  this  text. 

The  Initial  Series  on  the  Leyden  Plate  precedes  the  Initial  Series 
on  Stela  3  at  Tikal,  the  earfiest  contemporaneous  date  from  the 
monuments,  by  more  than  160  years,  and  wdth  the  possible  exception 
of  the  Tuxtla  Statuette  above  described,  probably  records  the  earfiest 
date  of  Maya  history.  It  should  be  noted  here  that  Cycle-8  Initial 
Series  are  occasionally  found  in  the  Dresden  Codex,  though  none  are 
quite  so  early  as  the  Initial  Series  from  the  Tuxtla  Statuette. 


MOELEY]      UsTTEODUCTIOIT  TO  STUDY  OF  MAYA  HIEROGLYPHS  199 

Passing  over  the  Initial  Series  whose  cycle  coefficient  is  9,  many  of 
which  have  already  been  described,  we  come  next  to  the  consideration 
of  Initial  Series  whose  cycle  coefficient  is  10,  a  very  limited  number 
indeed.  As  explained  in  Chapter  I,  the  southern  cities  did  not  long 
survive  the  opening  of  Cycle  10,  and  since  Initial-series  dating  did 
not  prevail  extensively  in  the  later  cities  of  the  north,  Initial  Series 
showing  10  cycles  are  very  unusual. 

In  figure  75,  is  shown  the  Initial  Series  from  the  Temple  of  the 
Initial  Series  at  Chichen  Itza,  the  great  metropolis  of  northern  Yucatan. 
This  inscription  is  not  found  on  a  stela  but  on  the  under  side  of  a  lintel 
over  a  doorway  leading  into  a  small  and  comparatively  insignificant 
temple.  The  introducing  glyph  appears  in  A1-B2  and  is  followed  by 
the  Initial-series  number  in  A3-A5.  The  student  will  have  little 
difficulty  in  deciphering  all  of  the  coefficients  except  that  belonging 
to  the  kin  in  A5,  which  is  a  head-variant  numeral,  and  the  whole 
number  will  be  found  to  read  10.2.9.1.?.  The  coefficient  of  the  day 
of  the  terminal  date  is  very  clearly  9  (see  B5)  and  the  month  part, 
7  Zac  (see  A6).  We  may  now  read  this  Initial  Series  as  10.2.9.1.  ?  9? 
7  Zac ;  in  other  words,  the  kin  coefficient  and  the  day  sign  are  still 
indeterminate.  First  substituting  0  as  the  missing  value  of  the  kin 
coefficient,  the  terminal  date  reached  will  be  10.2.9.1.0  13  Ahau  18 
Yax.  But  according  to  Table  XV,  position  18  Yax  is  just  9  days 
earlier  than  position  7  Zac,  the  month  part  recorded  in  A6.  Conse- 
quently, in  order  to  reach  7  Zac  from  10.2.9.1.0  13  Ahau  18  Yax,  9 
more  days  are  necessary.  Counting  these  forward  from  10.2.9.1.0 
13  Ahau  18  Yax,  the  date  reached  will  be  10.2.9.1.9  9  Muluc  7  Zac, 
which  is  the  date  recorded  on  this  lintel.  Compare  the  day  sign  with 
figure  16,  m,  n,  and  the  month  sign  with  figure  19,  s,  t. 

Two  other  Initial  Series  whose  cycle  coefficient  is  10  yet  remain  to 
be  considered,  namely,  Stelse  1  and  2  at  Quen  Santo. ^  The  first  of 
these  is  shown  in  figure  76,  A,  but  unfortunately  only  a  fragment  of 
this  monument  has  been  recovered.  In  A1-B2  appears  a  perfectly 
regular  form  of  the  introducing  glyph  (see  fig.  24),  and  this  is  followed 
in  A3-B4  by  the  Initial-series  number  itself,  with  the  exception  of 
the  kin,  the  glyph  representing  which  has  been  broken  off.  The 
student  will  readily  identify  A3  as  10  cycles,  noting  the  clasped  hand 
on  the  head-variant  period  glyph,  and  B3  as  2  katuns.  The  glyph 
in  A4  has  very  clearly  the  coefficient  5,  and  even  though  it  does  not 
seem  to  have  the  fleshless  lower  j  aw  of  the  tun  head,  from  its  position 
alone — after  the  unmistakable  katun  sign  in  B3 — we  are  perfectly 
justified  in  assuming  that  5  tuns  are  recorded  here.  Both  the  coeffi- 
cient and  the  glyph  in  B4  are  unfamiliar.    However,  as  the  former 

1  Tor  the  full  text  of  these  inscriptions,  see  Seler,  1902-1908:  n,  253,  and  1901  c:  i,  23,  fig.  7.  During  his 
last  visit  to  the  Maya  territory  the  writer  discovered  that  Stela  11  at  Tikal  has  a  Cycle-lO  Initial  Series, 
namely,  10.2.0.0.0.  3  Ahau  3  Ceh. 


200  BUREAU  OF  AMEEICAN  ETHNOLOGY  [bull.  57 

must  be  one  of  the  numerals  0  to  19,  inclusive,  since  it  is  not  one  of 
the  numerals  1  to  19,  inclusive,  it  is  clear  that  it  must  be  a  new  form 
for  0.  The  sign  to  "which  it  is  attached  bears  no  resemblance  to  either 
the  normal  form  for  the  uinal  or  the  head  variant;  but  since  it  occu- 
pies the  4th  position  after  the  introducing  glyph,  B4,  we  are  justified 
in  assuming  that  0  uinals  are  recorded  here.  Beyond  this  we  can 
not  proceed  with  certainty,  though  the  values  for  the  missing  parts 


A  B 

Fig.  76.  The  Cycle-10  Initial  Series  from  Quen  Santo  (from  drawings):  A,  Stela  1;  B,  Stela  2.  There  is 
less  than  a  year's  difference  in  time  between  the  Chichen  Itza  Initial  Series  and  the  Initial  Series  in  B. 


suggested  below  are  probably  those  recorded  on  the  lost  fragments 
of  the  monument.  As  recorded  in  A3-B4  this  number  reads 
10.2.5.0.  ?.  Now,  if  we  assume  that  the  missing  term  is  filled  with  0, 
we  shall  have  recorded  the  end  of  an  even  hotun  in  the  Long  Count, 
and  this  monument  becomes  a  regular  hotun-marker.  That  this 
monument  was  a  hotun-marker  is  corroborated  by  the  fact  that  Stela 
2  from  Quen  Santo  very  clearly  records  the  close  of  the  hotun  next 
after  10.2.5.0.0,  which  the  writer  beUeves  this  monument  marks.  For 


MOKLBY]      INTRODUCTION  TO  STUDY  OP  MAYA  HIEROGLYPHS  201 

this  reason  it  seems  probable  that  the  glyph  which  stood  in  Ao 
recorded  0  kins. 

Reducing  this  number  to  units  of  the  first  order  by  means  of  Table 
XIII,  we  obtain: 


A3  = 

10  X 144, 

000  = 

1,  440,  000 

B3^ 

2X  7, 

200  = 

14, 400 

A4  = 

5X 

360  = 

1,800 

B4  = 

OX 

20  = 

0 

A5'  = 

OX 

1  = 

0 

1,  456,  200 

Deducting  from  this  number  all  the  Calendar  Rounds  possible,  76 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and  141, 
respectively)  to  the  remainder,  the  terminal  date  reached  will  be 
9  Ahau  18  Yax,  and  the  whole  Initial  Series  originally  recorded  on 
this  monument  was  probably  10.2.5.0.0  9  Ahau  18  Yax. 

In  figure  76,  B,  is  shown  Stela  2  from  Quen  Santo.  The  workman- 
ship on  this  monument  is  somewhat  better  than  on  Stela  1  and,  more- 
over, its  Initial  Series  is  complete.  The  introducing  glyph  appears 
in  A1-B2  and  is  followed  by  the  Initial-series  number  in  A3-A5. 
Again,  10  cycles  are  very  clearly  recorded  in  A3,  the  clasped  hand 
of  the  cycle  head  still  appearing  in  spite  of  the  weathering  of  this 
glyph.  The  katun  sign  in  B3  is  almost  entirely  effaced,  though 
sufiB-cient  traces  of  its  coefficient  remain  to  enable  us  to  identify  it 
as  2.  Note  the  position  of  the  uneffaced  dot  with  reference  to  the 
horizontal  axis  of  the  glyph.  Another  dot  the  same  distance  above 
the  axis  would  come  as  near  the  upper  left-hand  corner  of  the  glyph- 
block  as  the  uneffaced  dot  does  to  the  lower  left-hand  corner.  More- 
over, if  3  had  been  recorded  here  the  uneffaced  dot  would  have  been 
nearer  the  bottom.  It  is  clear  that  1  and  4  are  quite  out  of  the 
question  and  that  2  remains  the  only  possible  value  of  the  numeral 
here.  We  are  justified  in  assuming  that  the  effaced  period  glyph 
was  the  katun  sign.  In  A4  10  tuns  are  very  clearly  recorded;  note 
the  fleshless  lower  jaw  of  the  tun  head.  The  uinal  head  with  its 
characteristic  mouth  curl  appears  in  B4.  The  coefficient  of  this  latter 
glyph  is  identical  with  the  uinal  coefficient  in  the  preceding  text 
(see  fig.  76,  A)  in  B4,  which  we  there  identified  as  a  form  for  0. 
Therefore  we  must  make  the  same  identification  here,  and  B4  then 
becomes  0  uinals.  From  its  position,  if  not  from  its  appearance,  we 
are  justified  in  designating  the  glyph  in  A5  the  head  for  the  kin 
period;  since  the  coefficient  attached  to  this  head  is  the  same  as  the 
one  ia  the  preceding  glyph  (B4),  we  may  therefore  conclude  that  0 
kins  are  recorded  here.    The  whole  number  expressed  in  A3-A5  is 


1  Missing. 


202 


BUREAU  OF  AMEEICAN  ETHNOLOGY 


[bull.  57 


therefore  10.2.10.0.0.  Reducing  this  to  units  of  the  first  order  by 
means  of  Table  XIII,  we  have: 


Deducting  from  this  number  all  the  Calendar  Rounds  possible,  76 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and  141, 
respectively)  to  the  remainder,  the  terminal  date  reached  will  be 
2  Ahau  13  Chen.  Although  the  day  sign  in  B5  is  effaced,  the  coeffi- 
cient 2  appears  quite  clearly.  The  month  glyph  is  recorded  in  A6. 
The  student  will  have  little  difficulty  in  restoring  the  coefficient  as 
13,  and  the  month  glyph  is  certainly  either  Chen,  Yax,  Zac,  or  Ceh 
(compare  fig.  19,  o  and  p,  q  and  r,  s  and  t,  and  u  and  v,  respectively). 
Moreover,  since  the  month  coefficient  is  13,  the  day  sign  in  B5  can 
have  been  only  Chicchan,  Oc,  Men,  or  Ahau  (see  Table  VII) ;  since  the 
kin  coefficient  in  A5  is  0,  the  effaced  day  sign  must  have  been  Ahau. 
Therefore  the  Initial  Series  on  Stela  2  at  Quen  Santo  reads  10.2.10.0.0 
2  Ahau  13  Chen  and  marked  the  hotun  immediately  following  the 
hotun  commemorated  by  Stela  1  at  the  same  site. 

The  student  will  note  also  that  the  date  on  Stela  2  at  Quen  Santo 
is  less  than  a  year  later  than  the  date  recorded  by  the  Initial  Series 
on  the  Temple  lintel  from  Chichen  Itza  (see  fig.  75,  B).  And  a  glance 
at  the  map  in  plate  1  will  show,  further,  that  Chichen  Itza  and  Quen 
Santo  are  separated  from  each  other  by  almost  the  entire  length 
(north  and  south)  of  the  Maya  territory,  the  former  being  in  the 
extreme  northern  part  of  Yucatan  and  the  latter  considerably  to  the 
south  of  the  central  Maya  cities.  The  presence  of  two  monuments 
so  close  together  chronologically  and  yet  so  far  apart  geographically 
is  difficult  to  explain.  Moreover,  the  problem  is  further  complicated 
by  the  fact  that  not  one  of  the  many  cities  lying  between  has  yielded 
thus  far  a  date  as  late  as  either  of  these.^  The  most  logical 
explanation  of  this  interesting  phenomenon  seems  to  be  that  while 
the  main  body  of  the  Maya  moved  northward  into  Yucatan  after 
the  collapse  of  the  southern  cities  others  retreated  southward  into 
the  highlands  of  Guatemala;  that  while  the  northern  emigrants 

1  At  Seibal  a  Period-ending  date  10.1.0.0.0  5  Ahau  3  Kayab  is  clearly  recorded,  but  this  is  some  30  years 
earlier  than  either  of  the  Initial  Series  here  under  discussion,  a  significant  period  just  at  this  particular 
epoch  of  Maya  history,  which  we  have  every  reason  to  believe  was  filled  with  stirring  events  and  quickly 
shifting  scenes.  Tikal,  with  the  Initial  Series  10.2.0.0.0  3  Ahau  3  Ceh,  and  Seibal  with  the  same  date 
(not  as  an  Initial  Series,  however)  are  the  nearest,  though  even  these  fall  10  years  short  of  the  Quen 
Santo  and  Chichen  Itza  Initial  Series. 


A3  =  10  X  144,  000 
B3=  2X  7,200 
A4  =  10  X  360 
B4=  OX  20 
A5=  OX  1 


1,  440,  000 
14,  400 
3,  600 
0 
0 


1,  458,  000 


MOELET]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


203 


were  colonizing  Yucatan  the  southern  branch  was  hxjdng  the  founda- 
tion of  the  civiUzation  which  was  to  flourish  later  under  the  name  of 
the  Quiche  and  other  allied  peoples;  and  finally,  that  as  Chichen  Itza 
was  a  later  northern  city,  so  Quen  Santo  was  a  later  southern 
site,  the  two  being  at  one  period  of  their  existence  at  least  approxi- 
mately contemporaneous,  as  these  two  Initial  Series  show. 

It  should  be  noted  in  this  connection  that  Cycle-10  Initial  Series 
are  occasionally  recorded  in  the  Dresden  Codex,  though  the  dates  in 
these  cases  are  all  later  than  those  recorded  on  the  Chichen  Itza  lintel 
and  the  Quen  Santo  stelse.  Before  closing  the  presentation  of  Initial- 
series  texts  it  is  first  necessary  to  discuss  two  very  unusual  and  highly 
irregular  examples  of  this  method  of  dating,  namely,  the  Initial  Series 
from  the  east  side  of  Stela  C  at  Quirigua  and  the  Initial  Series  from 
the  tablet  in  the  Temple  of  the  Cross  at  Palenque.  The  dates 
recorded  in  these  two  texts,  so  far  as  known,^  are  the  only  ones  which 
are  not  counted  from  the  starting  point  of  Maya  chronology,  the  date 
4  Ahau  8  Cumhu. 

In  figure  77,  ^,  is  shown  the  Initial  Series  on  the  east  side  of  Stela  C 
at  Quirigua.^  The  introducing  glyph  appears  in  A1-B2,  and  is  fol- 
lowed by  the  Initial-series  number  in  A3-A5.  The  student  will  easily 
read  this  as  13.0.0.0.0.  Keducing  this  number  to  units  of  the  first 
order  by  means  of  Table  XIII,  we  have: 


A3  = 

13X144, 

000  = 

1,  872,  000 

B3  = 

OX  7, 

200  = 

0 

A4  = 

OX 

360  = 

0 

B4  = 

OX 

20  = 

0 

A5  = 

ox 

1  = 

0 

1,  872,  000 

Deducting  from  this  number  all  the  Calendar  Rounds  possible,  98  ^ 
(see  Table  XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and 
141),  respectively,  to  the  remainder,  the  terminal  date  reached  should 
be,  under  ordinary  circumstances,  4  Aliau  3  Kankin.  An  inspection 
of  our  text,  howeyer,  will  show  that  the  terminal  date  recorded  in 
B5-A6  is  unmistakably  4  Ahau  8  Cumhu,  and  not  4  Ahau  3  Kankin. 
The  month  part  in  A6  is  unusually  clear,  and  there  can  be  no  doubt 

1  Up  to  the  present  time  no  successful  interpretation  of  the  inscription  on  Stela  C  at  Copan  has  been 
advanced.  The  inscription  on  each  side  of  this  monument  is  headed  by  an  introducing  glyph,  but  in 
neither  case  is  this  followed  by  an  Initial  Series.  A  number  consisting  of  n.14.5.1.0  is  recorded  in  connec- 
tion with  the  date  6  Ahau  18  Kayab,  but  as  this  date  does  not  appear  to  be  fixed  in  the  Long  Count,  there 
is  no  way  of  ascertaining  whether  it  is  earlier  or  later  than  the  starting  point  of  Maya  chronology.  Mr.  Bow- 
ditch  (1910:  pp.  195-196)  offers  an  interestmg  explanation  of  this  monument,  to  which  the  student  is 
referred  for  the  possible  explanation  of  this  text.  A  personal  inspection  of  this  inscription  failed  to 
confirm,  however,  the  assumption  on  which  Mr.  Bowditch's  conclusions  rest.  For  the  full  text  of  this 
inscription,  see  Maudslay,  1889-1902:  i,  pis.  39-41. 

2  For  the  full  text  of  this  inscription,  see  ibid. :  n,  pis.  16, 17, 19. 

3  Table  XVI  contains  only  80  Calendar  Rounds  (1,518,400),  but  by  adding  18  Calendar  Rounds  (341,640) 
the  number  to  be  subtracted,  98  Calendar  Rounds  (1,860,040),  will  be  reached. 


204 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


that  it  is  8  Cumhu.  Compare  A6  with  figure  19,  ,  V .  If  *we  have 
made  no  mistake  in  calculations,  then  it  is  evident  that  13.0.0.0.0 
counted  forward  from  the  starting  point  of  Maya  chronology,  4  Aliau 
8  Cumhu,  will  not  reach  the  terminal  date  recorded.  Further,  since 
the  coimt  in  Initial  Series  has  never  been  known  to  be  backward,* 
we  are  forced  to  accept  one  of  two  conclusions:  Either  the  starting 
point  is  not  4  Ahau  8  Cumliu,  or  there  is  some  error  in  the  original  text. 

However,  there  is  one  way  by 
means  of  which  we  can  ascer- 
tain the  date  from  which  the 
number  13.0.0.0.0  is  counted. 
The  terminal  date  reached  by 
the  count  is  recorded  very 
clearly  as  4  Ahau  8  Cumliu. 
Now,  if  we  reverse  our  op- 
eration and  count  the  given 
number,  13.0.0.0.0,  hackward 
from  the  known  terminal  date, 
4  Ahau  8  Cumliu,  we  reach  the 
starting  point  from  which  the 
count  proceeds. 

Deducting  from  this  num- 
ber, as  before,  all  the  Calen- 
dar Rounds  possible,  98  (see 
p.  203,  footnote  3),  and  ap- 
plying rules  1,  2,  and  3  (pp. 
139,  140,  141,  respectively) 
to  the  remainder,  remember- 
ing that  in  each  operation  the 
direction  of  the  count  is  haclc- 
ward,  not  forward,  the  starting 
point  will  be  found  to  be  4 
A  B  Ahau  8  Zotz.    This  is  the  first 

Fig.  77.  Initial  Series  which  proceed  from  a  date  prior  Initial  ScricS  yet  eUCOUntercd 

to  4  Ahau  8  Cumhu,  the  starting  point  of  Maya  chro-  .  ,    ,                            j   j  i? 

nology:  A,  Stela  C  (east  side)  at  Quirigua;  B,  Tern-  Wluch  haS  not  proceeded  trom 

pie  of  the  Cross  at  Palenque.  (J^tc  4  AhaU  8  Cumhu,  and 

until  the  new  starting  pomt  here  indicated  can  be  substantiated  it 
will  be  well  to  accept  the  correctness  of  this  text  only  with  a  reser- 
vation. The  most  we  can  say  at  present  is  that  if  the  number  re- 
corded in  A3-A5,  13.0.0.0.0,  be  counted  forward  from  4  Ahau  8  Zotz 
as  a  starting  point,  the  terminal  date  reached  by  calculation  will 
agree  with  the  terminal  date  as  recorded  in  B5~A6,  4  Ahau  8  Cumhu. 


1  Counting  13.0.0.0.0  backward  frona  the  starting  point  of  Maya  chronology,  4  Ahau  8  Cumhu,  gives  the 
date  4  Ahau  8  Zotz,  which  is  no  nearer  the  terminal  date  recorded  in  B5-A6  than  the  date  4  Ahau  3  Kan- 
kin  reached  by  counting  forward. 


MOKLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  205 

Let  US  next  examine  the  Initial  Series  on  the  tablet  from  the 
Temple  of  the  Cross  at  Palenque,  which  is  shown  in  figure  77,  B} 
The  introducing  glyph  appears  in  A1-B2,  and  is  followed  by  the 
Initial-series  number  in  A3-B7.  The  period  glyphs  in  B3,  B4,  B5, 
B6,  and  B7  are  all  expressed  by  their  corresponding  normal  forms, 
which  will  be  readily  recognized.  Passing  over  the  cycle  coefficient 
in  A3  for  the  present,  it  is  clear  that  the  katun  coefficient  in  A4  is  19. 
Note  the  dots  around  the  mouth,  characteristic  of  the  head  for  9  (fig. 
52,  g-l),  and  the  fleshless  lower  jaw,  the  essential  element  of  the  head 
for  10  (fig.  52,  m-r).  The  combination  of  the  two  gives  the  head  in 
A4  the  value  of  19.  The  tun  coefficient  in  A5  is  equally  clear  as  13. 
Note  the  banded  headdress,  characteristic  of  the  head  for  3  (fig.-  51, 
7i,  i),  and  the  fleshless  lower  jaw  of  the  10  head,  the  combination  of 
the  two  giving  the  head  for  13  (fig.  52,  w)?  The  head  for  4  and  the 
hand  zero  sign  appear  ,  as  the  coefficient  of  the  uinal  and  kin  signs  in  A6 
and  A7,  respectively.  The  number  will  read,  therefore,  ?.  19. 13.4.0. 
Let  us  examine  the  cycle  coefficient  in  A3  again.  The  natural  assump- 
tion, of  course,  is  that  it  is  9.  But  the  dots  characteristic  of  the  head 
for  9  are  not  to  be  found  here.  As  this  head  has  no  fleshless  lower 
jaw,  it  can  not  be  10  or  any  number  above  13,  and  as  there  is  no 
clasped  hand  associated  with  it,  it  can  not  signify  0,  so  we  are  limited 
to  the  numbers,  1,  2,  3,  4,  5,^  6,  7,  8,  11,  12,  and  13,  as  the  numeral 
here  recorded.  Comparing  this  form  with  these  numerals  in  figures 
51  and  52,  it  is  evident  that  it  can  not  be  1,  3,  4,  5,  6,  7,  8,  or  13,  and 
that  it  must  therefore  be  2,  11,  or  12.  Substituting  these  three  values 
in  turn,  we  have  2.19.13.4.0,  11.19.13.4.0,  and  12.19.13.4.0  as  the 
possible  numbers  recorded  in  A3-B7,  and  reducing  these  numbers  to 
units  of  the  first  order  and  deducting  the  highest  number  of  Calendar 
Eounds  possible  from  each,  and  applying  rules  1,  2,  and  3  (pp.  139, 
140,  and  141,  respectively)  to  their  remainders,  the  terminal  dates 
reached  will  be: 

2.19.13.4.0  5  Aliau  3  Pax 
11.19.13.4.0  9  Ahau  8  Yax 
12.19.13.4.0    8  Aliau  13  Pop 

If  this  text  is  perfectly  regular  and  our  calculations  are  correct,  one 
of  these  three  terminal  dates  will  be  found  recorded,  and  the  value 
of  the  cycle  coefficient  in  A3  can  be  determined. 

The  terminal  date  of  this  Initial  Series  is  recorded  in  A8-B9  and 
the  student  will  easily  read  it  as  8  Ahau  18  Tzec.    The  only  difference 

1  For  the  full  text  of  this  inscriptioB,  see  Maudslay,  1889-1902:  iv,  pis.  73-77. 

2  As  noted  in  Chapter  IV,  this  is  one  of  the  only  two  heads  for  13  found  in  the- inscriptions  which  is 
composed  of  the  essential  element  of  the  10  head  applied  to  the  3  head,  the  combination  of  the  two  giv- 
ing 13.  Usually  the  head  for  13  is  represented  by  a  form  peculiar  to  this  number  alone  and  is  not  built  up 
by  the  combination  of  lower  numbers  as  in  this  case. 

3  Although  at  first  sight  the  headdress  resembles  the  tun  sign,  a  closer  examination  shows  that  it  is 
not  this  element. 


206 


BUREAU  OF  AMEEICAN  ETHNOLOGY 


[BULL.  57 


between  the  day  coefficient  and  the  month  coefficient  is  that  the  latter 
has  a  fleshless  lower  jaw,  increasing  its  value  by  10.  Moreover,  com- 
parison of  the  month  sign  in  B9  with  g  and  li,  figure  19,  shows  unmis- 
takably that  the  month  here  recorded  is  Tzec.  But  the  terminal 
date  as  recorded  does  not  agree  with  any  one  of  the  three  above 
terminal  dates  as  reached  by  calculation  and  we  are  forced  to  accept 
one  of  the  two  conclusions  which  confronted  us  in  the  preceding  text 
(fig.  77,  A) :  Either  the  starting  point  of  this  Initial  Series  is  not  the 
date  4  Ahau  8  Cumhu,  or  there  is  some  error  in  the  original  text.^ 

Assuming  that  the  ancient  scribes  made  no  mistakes  in  this  inscrip- 
tion, let  us  count  backward  from  the  recorded  terminal  date,  8  Ahau 
18  Tzec,  each  of  the  three  numbers  2.19.13.4.0,  11.19.13.4.0,  and 
12.19.13.4.0,  one  of  which,  we  have  seen,  is  recorded  in  A3-B7. 

Reducing  these  numbers  to  units  of  the  first  order  by  means  of 
Table  XIII,  and  deducting  all  the  Calendar  Rounds  possible  from 
each  (see  Table  XVI),  and,  finally,  applying  rules  1,2,  and  3  (pp.  139, 
140,  and  141,  respectively),  to  the  remainders,  the  starting  points  wiU 
be  found  to  be : 

7  Ahau  3  Mol  for  2.19.13.4.0 

3  Ahau  18  Mac  for  11.19.13.4.0 

4  Ahau  8  Zotz  for  12.19.13.4.0 

Which  of  these  starting  points  are  we  to  accept  as  the  one  from  which 
this  number  is  counted?  The  correct  answer  to  this  question  will 
give  at  the  same  time  the  value  of  the  cycle  coefficient,  which,  as 
we  have  seen,  must  be  2,  11,  or  12.  Most  Maya  students  have 
accepted  as  the  starting  point  of  this  Initial-series  number  the  last 
of  the  three  dates  above  given,  4  Ahau  8  Zotz,  which  involves  also  the 
identification  of  the  cycle  coefficient  in  A3  as  12.  The  writer  has 
reached  the  same  conclusion  from  the  following  points : 

1.  The  cycle  coefficient  in  A3,  except  for  its  very  unusual  headdress, 
is  almost  identical  with  the  other  two  head-variant  numerals,  whose 
values  are  known  to  be  12.  These  three  head  numerals  are  shown 
side  by  side  in  figure  52,  t-v,  t  being  the  form  in  A3  above,  inserted 
in  this  figure  for  the  sake  of  comparison.  Although  these  three  heads 
show  no  single  element  or  characteristic  that  is  present  in  all  (see  p. 
100),  each  is  very  similar  to  the  other  two  and  at  the  same  time  is 
dissimilar  from  all  other  head-variant  numerals.  This  fact  warrants 
the  conclusion  that  the  head  in  A3  represents  the  numeral  12,  and  if 
this  is  so  the  starting  point  of  the  Initial  Series  under  discussion  is 
4  Ahau  8  Zotz. 

2.  Aside  from  the  fact  that  12  seems  to  be  the  best  reading  of  the 
head  in  A3,  and  consequently  that  the  starting  point  of  this  number 
is  4  Ahau  8  Zotz,  the  writer  believes  that  4  Ahau  8  Zotz  should  be 


1  Similarly,  it  could  be  shown  that  the  use  of  every  other  possible  value  of 
not  give  the  terruinal  date  actually  recorded. 


the  cycle  coefficient  will 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57    PLATE  16 


INITIAL  SERIES  AND  SECONDARY  SERIES  ON   LINTEL  21,  YAXCHILAN 


MORLEY]      INTRODUCTION  TO  STUDY  Or  MAYA  HIEROGLYPHS 


207 


selected,  if  for  no  other  reason  than  that  another  Initial  Series  lias 
been  found  which  proceeds  from  this  same  date,  while  no  oth(M^  Initial 
Series  Imown  is  counted  from  either  7  Ahau  3  Mol  or  3  Ahau  18  Mac. 

As  we  have  seen  in  discussing  the  preceding  text,  from  the  east  side 
of  Stela  C  at  Quirigua  (fig.  77,  A),  the  Initial  Series  there  recorded 
was  counted  from  the  same  starting  point,  4  Ahau  8  Zotz,  as  the  Initial 
Series  from  the  Temple  of  the  Cross  at  Palenque,  if  we  read  the  latter 
as  12.19.13.4.0.  This  coincidence,  the  writer  believes,  is  sufficient  to 
warrant  the  identification  of  the  head  in  A3  (fig.  77,  B)  as  the  head 
numeral  12  and  the  acceptance  of  this  Initial  Series  as  proceeding 
from  the  same  starting  point  as  the  Quirigua  text  just  described, 
namely,  the  date  4  Ahau  8  Zotz.  With  these  two  examples  the  dis- 
cussion of  Initial-series  texts  will  be  closed. 

Texts  He  cording  Initial  Series  and  Secondary  Series 

It  has  been  explained  (see  pp.  74-76)  that  in  addition  to  Initial- 
series  dating  the  Maya  had  another  method  of  expressing  their 
dates,  known  as  Secondary  Series,  which  was  used  when  more  than 
one  date  had  to  be  recorded  on  the  same  monument.  It  was  stated, 
further,  that  the  accuracy  of  Secondary- series  dating  depended  solely 
on  the  question  whether  or  not  the  Secondary  Series  was  referred  to 
some  date  whose  position  in  the  Long  Count  was  fixed  either  by  the 
record  of  its  Initial  Series  or  in  some  other  way.  The  next  class  of  texts 
to  be  presented  will  be  those  showing  the  use  of  Secondary  Series  in 
connection  with  an  Initial  Series,  by  means  of  which  the  Initial-series 
values  of  the  Secondary-series  dates,  that  is,  their  proper  positions 
in  the  Long  Count,  may  be  worked  out  even  though  they  are  not 
recorded  in  the  text. 

The  first  example  presented  will  be  the  inscription  on  Lintel  21  at 
Yaxchilan,  which  is  figured  in  plate  16.^  As  usual,  when  an  Initial 
Series  is  recorded,  the  introducing  glyph  opens  the  text  and  this  sign 
appears  in  Al,  being  followed  by  the  Initial-series  number  itself  in 
B1-B3.  This  the  student  will  readily  decipher  as  9.0.19.2.4,  record- 
ing apparently  a  very  early  date  in  Maya  history,  within  20  years  of 
9.0.0.0.0  8  Ahau  13  Ceh,  the  date  arbitrarily  fixed  by  the  writer  as 
the  opening  of  the  first  great  period. 

Reducing  this  number  by  means  of  Table  XIII  to  units  of  the  first 
order  ^  and  deducting  all  the  Calendar  Rounds  possible,  68  (see  Table 
XVI),  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and  141,  respec- 
tively) to  the  remainder,  the  terminal  date  reached  will  be  2  Kan  2 
Yax.  This  date  the  student  will  find  recorded  in  A4  and  A7a,  glyph 
B6b  being  the  month-sign  'indicator,"  or  the  closmg  glyph  of  the 

1  For  the  full  text  of  this  inscription  see  Maler,  1903:  n,  No.  2,  pi.  56. 

2  From  this  point  on  this  step  wUl  be  omitted,  but  the  student  is  urged  to  perform  the  calculations 
necessary  ia  each  case  to  reach  the  terminal  dates  recorded, 


208 


BUREAU  OF  AMEEICAN  ETHNOLOGY 


[bull.  57 


Supplementary  Series,  here  shown  mth  the  coefficient  9.  Compare 
the  day  sign  in  A4a  with  the  sign  for  Kan  in  figure  16,/,  and  the  month 
sign  in  A7a  with  the  sign  for  Yax  in  figure  19,  g',  r.  We  have  then 
recorded  in  Al-A4^,  and  A7a  the  Initial-series  date  9.0.19.2.4  2  Kan 
2  Yax.  At  first  sight  it  would  appear  that  this  early  date  indicates 
the  time  at  or  near  which  this  lintel  was  inscribed,  bu  t  a  closer  exami- 
nation reveals  a  different  condition.  Following  along  through  the 
glyphs  of  this  text,  there  is  reached  in  C3-C4  still  another  number  in 
which  the  normal  forms  of  the  katun,  tun,  and  uinal  signs  clearly 
appear  in  connection  with  bar  and  dot  coefficients.  The  question  at 
once  arises.  Has  the  number  recorded  here  anything  to  do  with  the 
Initial  Series,  which  precedes  it  at  the  beginning  of  this  text? 

Let  us  first  examine  this  number  before  attempting  to  answer  the 
above  question.  It  is  apparent  at  the  outset  that  it  differs  from  the 
Initial-series  numbers  previously  encountered  in  several  respects: 

1.  There  is  no  introducing  glyph,  a  fact  which  at  once  eliminates 
the  possibility  that  it  might  be  an  Initial  Series. 

2.  There  is  no  kin  period  glyph,  the  uinal  sign  in  C3  having  two 
coefficients  instead  of  one. 

3.  The  order  of  the  period  gl3rphs  is  reversed,  the  highest  period, 
here  the  katim,  closing  the  series  instead  of  commencing  it  as  here- 
tofore. 

It  has  been  explained  (see  p.  129)  that  in  Secondary  Series  the 
order  of  the  period  glyphs  is  almost  invariably  the  reverse  of  that 
shown  by  the  period  glyphs  in  Initial  Series;  and  further,  that  the 
former  are  usually  presented  as  ascending  series,  that  is,  with  the 
lowest  imits  first,  and  the  latter  invariably  as  descending  series,  with 
the  highest  units  first.  It  has  been  explained  also  (see  p.  128)  that 
in  Secondary  Series  the  kin  period  glyph  is  usually  omitted,  the  kin 
coefficient  being  attached  to  the  left  of  the  uinal  sign.  Since  both 
of  these  points  (see  2  and  3,  above)  are  characteristic  of  the  number 
in  C3-C4,  it  is  probable  that  a  Secondary  Series  is  recorded  here,  and 
that  it  expresses  5  kins,  16  uinals,  1  tun,  and  15  katuns.  Reversing 
this,  and  writing  it  according  to  the  notation  followed  by  most  Maya 
students  (see  p.  138,  footnote  1),  we  have  as  the  number  recorded  by 
C3-C4,  15.1.16.5. 

Reducing  this  number  to  units  of  the  first  order  by  means  of  Table 
XIII,  we  have: 

C4  =15X7,200  =  108,000 
D3=  IX  360=  360 
C3  =16X  20=  320 
C3  =  5  X        1  =  5 

108,  685, 


1  Since  the  introducing  glyph  always  accompanies  an  Initial  Series,  it  has  here  been  included  as  a  part 
of  it,  though,  as  has  been  explained  elsewhere,  its  function  is  unknown. 


MOKLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  209 
9 

Since  all  the  Calendar  Rounds  which  this  number  contains,  5  (see 
Table  XVI)  may  be  deducted  from  it  wi+hout  affecting  its  value,  we 
can  further  reduce  it  to  13,785  (108,685-94,900),  and  this  will  be  the 
number  used  in  the  following  calculations. 

It  was  stated  (on  p.  135)  in  describing  the  direction  of  the  count 
that  numbers  are  usually  counted  forward  from  the  dates  next  pre- 
ceding them  in  a  text,  although  this  is  not  invariably  true.  Applying 
this  rule  to  the  present  case,  it  is  probable  that  the  Secondary-series 
number  15.1.16.5,  which  we  have  reduced  to  13,785  units  of  the  first 
order,  is  counted  forward  from  the  date  2  Kan  2  Yax,  the  one  next 
preceding  it  in  our  text,  a  date,  moreover,  the  Initial-series  value  of 
which  is  known. 

Remembering  that  this  date  2  Kan  2  Yax  is  our  new  starting  point, 
and  that  the  count  is  forward,  by  applying  rules  1,  2,  and  3  (pp.  139, 
140,  and  141,  respectively),  to  13,785,  the  new  terminal  date  reached 
will  be  7  Mnluc  17  Tzec;  and  this  date  is  recorded  in  C5-D5.  Compare 
C5  with  the  sign  for  the  day  Muluc  in  figure  16,  m,  n,  and  D5  with 
the  sign  for  the  month  Tzec  in  figure  19,  g,  Ji.  Furthermore,  by  add- 
ing the  Secondary-series  number  15.1.16.5  to  9.0.19.2.4  (the  Initial- 
series  number  which  fixes  the  position  of  the  date  2  Kan  2  Yax  in  the 
Long  Count),  the  Initial-series  value  of  the  terminal  date  of  the  Sec- 
ondary Series  (calculated  and  identified  above  as  7  Muluc  17  Tzec) 
can  also  be  determined  as  follows: 

9.  0.19.  2.4    2  Kan    2  Yax      Initial  Series 

15.  1.16.5  Secondary-series  number 

9.16.  1.  0.9  7  Muluc  17  Tzec  Initial  Series  of  the  Secondary- 
series  terminal  date  7  Muluc 
17  Tzec 

The  student  may  verify  the  above  calculations  by  treating  9.16.1.0.9 
as  a  new  Initial-series  number^  and  counting  it  forward  from  4  Ahau 
8  Cumhu,  the  starting  point  of  Maya  chronology.  The  terminal  date 
reached  will  be  found  to  be  the  same  date  as  the  one  recorded  in 
C5-D5j  namely,  7  Muluc  17  Tzec. 

What  is  the  meaning  then  of  this  text,  which  records  two  dates 
nearly  300  years  apart  ?  ^  It  must  be  admitted  at  the  outset  that  the 
nature  of  the  events  wliich  occurred  on  these  two  dates,  a  matter 
probably  Bet  forth  in  the  glyphs  of  unknown  meaning  in  the  text,  is 
totally  unknown.  It  is  possible  to  gather  from  other  sources,  how- 
everj  some  little  data  concerning  their  significance.  In  the  first  place, 
9.16.1.0.9  7  Muluc  17  Tzec  is  almost  surely  the  contemporaneous 
date"  of  this  lintel,  the  date  indicating  the  time  at  or  near  which  it 
was  formally  dedicated  or  put  into  use.  This  point  is  established 
almost  to  a  certainty  by  the  fact  that  all  the  other  dates  known  at 
Yaxchilan  are  very  much  nearer  to  9.16.1.0.9  7  Muluc  17  Tzec  in  point 


1  The  number  15.1.16.5  is  equal  to  108,685  days,  or  297^  years. 

43508°— Bull.  57—15  14 


210 


BUKEAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


of  time  than  to  9.0.19.2.4  2  Kan  2  Yax,  the  Initial-series  date  recorded 
on  this  lintel.  Indeed,  while  they  range  from  9  days  ^  to  75  years 
from  the  former,  the  one  nearest  the  latter  is  more  than  200 
years  later.  This  practically  proves  that  9.16.1.0.9  7  Muluc 
17  Tzec  indicates  the  ^^contemporaneous  time"  of  this  lintel  and  that 
9.0.19.2.4  2  Kan  2  Yax  referred  to  some  earlier  event  which  took 
place  perhaps  even  before  the  founding  of  the  city.  And  finally,  since 
this  inscription  is  on  a  luitel,  we  may  perhaps  go  a  step  further  and 
hazard  the  conclusion  that  9.16.1.0.9  7  Muluc  17  Tzec  records  the 
date  of  the  erection  of  the  structure  of  which  this  lintel  is  a  part. 

We  may  draw  from  this  inscription  a  conclusion  which  will  be 
found  to  hold  good  in  almost  all  cases,  namely,  that  the  last  date  in 
a  text  almost  always  indicates  the  ^^contemporaneous  time"  of  the 
monument  upon  which  it  appears.  In  the  present  text,  for  example, 
the  Secondary-series  date  7  Muluc  17  Tzec,  the  Initial-series  value 
of  which  was  found  to  be  9.16.1.0.9,  is  in  all  probability  its  contem- 
poraneous date,  or  very  near  thereto.  It  will  be  well  to  remember 
this  important  point,  since  it  enables  us  to  assign  monuments  upon 
which  several  different  dates  are  recorded  to  their  proper  periods  in 
the  Long  Count. 

The  next  example  illustrating  the  use  of  Secondary  Series  with  an 
Initial  Series  is  the  inscription  from  Stela  1  at  Piedras  Negras,  figured 
in  plate  17.^  The  order  of  the  gljrphs  in  this  text  is  somewhat  irreg- 
ular. It  will  be  noted  that  there  is  an  uneven  number  of  glyph 
columns,  so  that  one  column  will  have  to  be  read  by  itseK.  The 
natural  assumption  would  be  that  A  and  B,  C  and  D,  and  E  and  F 
are  read  together,  leaving  G,  the  last  column,  to  be  read  by  itself. 
This  is  not  the  case,  however,  for  A,  presenting  the  Initial  Series,  is 
read  first,  and  then  B  C,  D  E,  and  F  G,  in  pairs.  The  introducing 
glyph  of  the  Initial  Series  appears  in  Al  and  is  followed  by  the  Initial- 
series  number  9.12.2.0.16  in  A2-A6.  The  student  should  be  per- 
fectly familiar  by  this  time  with  the  processes  involved  in  counting 
tliis  number  from  its  starting  point,  and  should  have  no  difficulty  in 
determing  by  calculation  the  terminal  date  recorded  in  A7,  C2,  namely, 
6  Cib  14  Yaxkin.^  Compare  A7  with  the  sign  for  Cib  in  figure  16, 
and  C2  with  the  sign  for  Yaxkin  in  figure  19,  Ic,  I.  The  Initial  Series 
recorded  in  A1-A7,  C2  is  9.12.2.0.16  5  Cib  14  Yaxkin. 

Passing  over  the  glyphs  in  B3-E1,  the  meanings  of  which  are 
unknown,  we  reach  in  D2  E2  a  number  showing  very  clearly  the  tun 
and  uinal  signs,  the  latter  having  two  coefficients  instead  of  one. 
Moreover,  the  order  of  these  period  glyphs  is  reversed,  the  lower 
standing  first  in  the  series.    As  explained  in  connection  with  the  pre- 

ilt  is  interesting  to  note  in  this  connection  that  the  date  9.16.1.0.0  11  Ahau  8  Tzec,  which  is  within  9 
days  of  9.1G.1.0.9  7  Muluc  17  Tzec,  is  recorded  in  four  different  inscriptions  at  "Y  axchilan,  one  of  which  (see 
pi.  9,  A)  has  already  been  figured. 

2  For  the  full  text  of  this  inscription  see  Maler,  1901:  ii,  No.  1,  pi.  12. 

3  The  month-sign  indicator  appears  in  B2  with  a  coefficient  10. 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57    PLATE  17 


INITIAL  SERIES  AND  SECONDARY  SERIES  ON 
STELA   1,   PIEDRAS  NEGRAS 


MOELBY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  211 

ceding  text,  these  points  are  both  characteristic  of  Secondary-series 
numbers,  and  we  may  conclude  therefore  that  D2  E2  records  a  num- 
ber of  this  kind.  Finally,  since  the  kin  coefficient  in  Secondary 
Series  usually  appears  on  the  left  of  the  uinal  sign,  we  may  express 
this  number  in  the  commonly  accepted  notation  as  follows:  12.9.15. 
Reducing  this  to  units  of  the  first  order,  we  have : 

E2  =  12X360  =4,  320 
D2=  9X  20=  .180 
D2  =  15X    1=  15 


4,515 

Remembering  that  Secondary-series  numbers  are  usually  counted 
from  the  dates  next  preceding  them  in  the  texts,  in  this  case  5  Cib 
14  Yaxkin,  and  proceeding  according  to  rules  1,  2,  and  3  (pp.  139,  140, 
and  141,  respectively),  the  terminal  date  of  the  Secondary  Series' 
reached  will  be  9  Chuen  9  Kankin,  which  is  recorded  in  Fl  Gl,  though 
unfortunately  these  glyphs  are  somewhat  effaced.  Moreover,  since 
the  position  of  5  Cib  14  Yaxkin  in  the  Long  Count  is  known,  that  is, 
its  Initial-series  value,  it  is  possible  to  determine  the  Initial-series 
value  of  this  new  date,  9  Chuen  9  Kankin : 

9.12.  2.  0.16    5  Cib    14  Yaxkin 
12.  9.15 

9.12.14.10.11    9  Chuen  9  Kankin 

But  the  end  of  this  text  has  not  been  reached  with  the  date  9  Chuen 
9  Kankin  in  Fl  Gl.  Passing  over  F2  G2,  the  meanings  of  which  are 
unknown,  we  reach  in  F3  an  inverted  Abau  with  the  coefficient  5 
above  it.  As  explained  on  page  72,  this  probably  signifies  5  kins, 
the  inversion  of  the  glyph  changing  its  meaning  from  that  of  a  par- 
ticular day  sign,  Ahau,  to  a  general  sign  for  the  kin  day  period  (see 
fig.  34,  d).  The  writer  recalls  but  one  other  instance  in  which  the 
inverted  Abau  stands  for  the  kin  sign — on  the  north  side  of  Stela  C 
at  Quirigua. 

We  have  then  another  Secondary-series  number  consisting  of  5 
kins,  which  is  to  be  counted  from  some  date,  and  since  Secondary- 
series  numbers  are  usually  counted  from  the  date  next  preceding 
them  in  the  text,  we  a,re  justified  in  assuming  that  9  Chuen  9  Kankin 
is  our  new  starting  point. 

Counting  5  forward  from  this  date,  according  to  rules  1,  2,  and  3 
(pp.  139, 140,  and  141,  respectively ),  the  terminal  date  reached  will  be  1 
Cib  14  Kankin,  and  this  latter  date  is  recorded  in  G3-G4. .  Compare 
G3  with  the  sign  for  Cib  in  A7  a,nd  in  figure  16,  and  G4  with  the 
sign  for  Kankin  in  figure  19,  y,  z.  Moreover,  since  the  Initial-series 
value  of  9  Chuen  9  Kankin  was  calculated  above  as  9.12.14.10.11, 


212 


BUREAU  OF  AMEKICAN  ETHNOLOGY 


[BULL.  57 


the  Initial-series  value  of  this  new  date,  1  Cib  14  Kankin,  also  can 
be  calculated  from  it: 

9.12.14.10.11    9  Chuen  9  Kankin 
5 

9.12.14.10.16    1  Cib    14  Kankin 

Passing  over  G5  as  unknown,  we  reach  in  G6-G7  another  Secondary- 
series  number.  The  student  will  have  little  difficulty  in  identifying 
G6  as  2  uinals,  5  kms,  and  G7  as  1  katun.  It  will  be  noted  that  no 
tun  sign  appears  in  this  number,  which  is  a  very  unusual  condition. 
By  far  the  commoner  practice  in  such  cases  in  which  0  units  of  some 
period  are  involved  is  to  record  the  period  with  a  coefficient  0.  How- 
ever, this  was  not  done  in  the  present  case,  and  since  no  tuns  are 
recorded,  we  may  conclude  that  none  were  involved,  and  G6-G7 
may  be  written  1.(0). 2.5.  Reducing  this  number  to  units  of  the  first 
order,  we  have: 

G7  =  1  X7, 200  =  7,200 
0)  OX  360=  0 
G6  =  2X  20=  40 
G6  =  5X        1=  5 

7,  245 

Remembering  that  the  starting  point  from  which  this  number  i^ 
counted  is  the  date  next  precedmg  it,  1  Cib  14  Kankin,  and  applying 
rules  1,  2,  and  3  (pp.  139,  140,  and  141,  respectively),  the  terminal  dat(  i 
reached  will  be  6  Imix  19  Zac ;  this  latter  date  is  recorded  in  G8-G9  I 
Compare  G8  with  the  sign  for  Imix  in  figure  16,  a,  h,  and  G9  with  th 
sign  for  Zac  in  figure  19,  s,  t  Moreover,  since  the  Initial  Series  o 
1  Cib  14  Kankin  was  obtained  by  calculation  from  the  date  next  pre 
ceding  it,  the  Initial  Series  of  5  Imix  19  Zac  may  be  determined  in  th 
same  way. 

9.12.  14.10.16    1  Cib  14  Kankin 
1.   0.^2.  5 

9.13.  14.13.  1    5  Imix  19  Zac 

With  the  above  date  closes  the  kno\^Ti  part  of  tliis  text,  the  remainin 
glyphs,  G10-G12,  bemg  of  unknown  meaning. 

Assembling  all  the  glyphs  deciphered  above,  the  known  part  ( 
tliis  text  reads  as  follows : 

9.12.   2.  0.16    A1-A7,  C2    6  Cib  14  Yaxkin 

12.  9.15    D2  E2 
9.12.  14.10.11    Fl  Gl  9  Chuen  9  Kankin 

5  F3 

9.12.  14.10.16    G3  G4  1  Cib  14  Kankin 
1.   0}  2.  5    G6  G7 

9.13.  14.13.  1    G8  G9  5  Imix  19  Zac 


1  Not  expressed. 


BUREAU  OF  AMERICAN  ETHNOLOGY 


A 


INITIAL  SERIES  U)  AND  SECONDARY 


BULLETIN  57    PLATE  18 


B 


SERIES  (B)  ON  STELA  K,  QUIRIGUA 


MORLBY]      INTEODUCTIOlSr  TO  STUDY  OF  MAYA  HIEROGLYPHS  213 

We  have  recorded  here  four  different  dates,  of  which  the  last, 
9.13.14.13.1  5  Imix  19  Zac,  probably  represents  the  actual  date,  or 
very  near  thereto,  of  this  monument.^  The  period  covered  between 
the  first  and  last  of  these  dates  is  about  32  years,  within  the  range 
of  a  single  lifetime  or,  indeed,  of  the  tenure  of  some  important  office 
by  a  single  individual.  The  unknown  glyphs  again  probably  set  forth 
the  nature  of  the  events  which  occurred  on  the  dates  recorded. 

In  the  two  preceding  texts  the  Secondary  Series  given  are  regular 
in  every  way.  Not  only  was  the  count  forward  each  time,  but  it  also 
started  in  every  case  from  the  date  immediately  preceding  the  num- 
ber counted.  This  regularity,  however,  is  far  from  universal  in  Sec- 
ondary-series texts,  and  the  following  examples  comprise  some  of 
the  more  common  departures  from  the  usual  practice. 

In  plate  18  is  figured  the  Initial  Series  from  Stela  K  at  Quirigua.^ 
The  text  opens  on  the  north  side  of  this  monument  (see  pi.  18,  A) 
with  the  introducing  glyph  in  A1-B2.  This  is  followed  by  the  Initial- 
series  number  9.18.15.0.0  in  A3-B4,  which  leads  to  the  terminal  date 
3  Ahau  3  Yax.  The  day  part  of  this  date  the  student  will  find 
recorded  in  its  regular  position,  A5a.  Passing  over  A5b  and  B5,  the 
meanings  of  which  are  unknown,  we  reach  in  A6  a  Secondary-series 
number  composed  very  clearly  of  10  uinals  and  10  kins  (10.10),  which 
reduces  to  the  following  number  of  units  of  the  first  order: 

A6  =  10X20  =  200 
A6  =  10X  1=  10 

210 

The  first  assumption  is  that  this  number  is  counted  forward  from  the 
terminal  date  of  the  Initial  Series,  3  Ahau  3  Yax,  and  performing  the 
operations  indicated  in  rules  1,  2,  and  3  (pp.  139,  140,  and  141,  respec- 
tively) the  terminal  date  reached  will  be  5  Oc  8  Uo.  Now,  although 
the  day  sign  in  B6b  is  clearly  Oc  (see  fig.  16,  o-q),  its  coefficient  is 
very  clearly  1,  not  5,  and,  moreover,  the  month  in  A7a  is  unmistak- 
ably 18  Kayab  (see  fig.  19,  d'-f).  Here  then  instead  of  finding  the 
date  determined  by  calculation,  5  Oc  8  Uo,  the  date  recorded  is  1  Oc 
18  Kayab,  and  consequently  there  is  some  departure  from  the  prac- 
tices heretofore  encountered. 

Since  the  association  of  the  number  10.10  is  so  close  with  (1)  the 
terminal  date  of  the  Initial  Series,  3  Ahau  3  Yax,  and  (2)  the  date 
1  Oc  18  Kayab  almost  immediately  following  it,  it  would  almost  seem 
as  though  these  two  dates  must  be  the  startmg  point  and  terminal 
date,  respectively,  of  this  number.  If  the  count  is  forward,  we  have 
just  proved  that  this  can  not  be  the  case;  so  let  us  next  count  the 

1  The  writer  has  recently  established  the  date  of  this  monument  as  9. 13. 15. 0. 0  13  Ahau  18  Pax,  or  99 
days  later  than  the  above  date. 

2  For  the  full  text  of  this  inscription,  see  Maudslay,  1889-1902:  n,  pis.  47-49. 


214 


BUREAU  OF  AMEEICAN  ETHNOLOGY 


[bull.  57 


number  backward  and  see  whether  we  can  reach  the  date  recorded 
in  B6b-A7a  (1  Oc  18  Kayab)  in  this  way. 

Counting  210  backward  from  3  Ahau  3  Yax,  according  to  rules  1,  2, 
and  3  (pp.  139,  140,  and  141,  respectively),  the  terminal  date  reached 
will  be  1  Oc  18  Kayab,  as  recorded  in  B6b-A7.  In  other  words,  the 
Secondary  Series  in  this  text  is  counted  backward  from  the  Initial  Se- 
ries, and  therefore  precedes  it  in  point  of  time.  This  will  appear  from 
the  Initial-series  value  of  1  Oc  18  Kayab,  which  may  be  determined 
by  calculation: 

9.18.15.  0.  0    3  Ahau  3  Yax 
10.10 

9.18.14.  7.10    1  Oc  18  Kayab 

This  text  closes  on  the  south  side  of  the  monument  in  a  very  unusual 
manner  (see  pi.  18,  B).  In  B3a  appears  the  month-sign  indicator, 
here  recorded  as  a  head  variant  with  a  coefficient  10,  and  following 
immediately  in  B3b  a  Secondary-series  number  composed  of  0  uinals 
and  0  kins,  or,  in  other  words,  nothing.  It  is  obvious  that  in  count- 
ing this  number  0.0,  or  nothing,  either  backward  or  forward  from 
the  date  next  preceding  it  in  the  text,  1  Oc  18  Kayab  in  B6b-A7a  on 
the  north  side  of  the  stela,  the  same  date  1  Oc  18  Kayab  will  remain. 
But  this  date  is  not  repeated  in  A4,  where  the  terminal  date  of  this 
Secondary  Series,  0.0,  seems  to  be  recorded.  However,  if  we  count 
0.0  from  the  terminal  date  of  the  Initial  Series,  3  Ahau  3  Yax,  we  reach 
the  date  recorded  in  A4,  3  Ahau  3  Yax,^  and  this  whole  text  so  far  as 
deciphered  will  read: 

9.18.15.  0.  0    3  Ahau  3  Yax 
10.10  backward 

9.18.14.  7.10    1  Oc  18  Kayab 

0.  0    forward  from  Initial  Series 

9.18.15.  0.  0    3  Ahau  3  Yax 

The  reason  for  recording  a  Secondary-series  number  equal  to  zero, 
the  writer  beheves,  was  because  the  first  Secondary-series  date  1  Oc 
18  Kayab  precedes  the  Initial-series  date,  which  in  this  case  marks 
the  time  at  which  this  monument  was  erected.  Hence,  in  order  to 
have  the  closing  date  on  the  monument  record  the  contemporaneous 
time  of  the  monument,  it  was  necessary  to  repeat  the  Initial-series 
date;  this  was  accomplished  by  adding  to  it  a  Secondary-series  date 
denoting  zero.  Stela  K  is  the  next  to  the  latest  ho  tun-marker  at 
Quirigua  following  immediately  Stela  I,  the  Initial  series  of  which 
marks  the  hotun  ending  9.18.10.0.0  10  Ahau  8  Zac  (see  pi.  6,  O). 

Mr.  Bowditch  (1910 :  p.  208)  has  advanced  a  very  plausible  explana- 
tion to  account  for  the  presence  of  the  date  9.18.14.7.10  1  Oc  18  Kayab 

1  Although  the  details  of  the  day  and  month  signs  are  somewhat  effaced,  the  coefficient  in  each  case  is 
3,  agreeing  with  the  coefficients  in  the  Initial-series  terminal  date,  and  the  outline  of  the  month  glyph 
suggests  that  it  is  probably  Yax.   See  fig.  19,  q,  r. 


MOELET]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  215 


on  this  monument.  He  shows  that  at  the  time  when  Stehi  K  was 
erected,  namely,  9.18.15.0.0  3  Ahau  3  Yax,  the  official  calendar  had 
outrun  the  seasons  by  just  210  days,  or  exactly 
the  number  of  days  recorded  in  A6,  plate  18, 
(north  side) ;  and  further,  that  instead  of  being 
the  day  3  Yax,  which  occurred  at  Quirigua  about 
the  beginning  of  the  dry  season,^  in  reality  the 
season  was  210  days  behind,  or  at  18  Kayab, 
about  the  beginning  of  the  rainy  season.  This 
very  great  discrepancy  between  calendar  and 
season  could  not  have  escaped  the  notice  of  the 
priests,  and  the  210  days  recorded  in  A6  may 
well  represent  the  days  actually  needed  on  the 
date  9.18.15.0.0  3  Ahau  3  Yax  to  bring  the  calen- 
dar into  harmony  with  the  current  season.  If 
this  be  true,  then  the  date  9.18.14.7.0  1  Oc  18 
Kayab  represented  the  day  indicated  by  the  sun 
when  the  calendar  showed  that  the  3d  ho  tun  in 
Katun  18  of  Cycle  9  had  been  completed.  Mr. 
Bowditch  suggests  the  following  free  interpreta- 
tion of  this  passage:  '^The  sun  has  just  set  at 
its  northern  point  ^  and  we  are  counting  the  day 
3  Yax — 210  days  from  18  Kayab — which  is  the 
true  date  in  the  calendar  according  to  our  tra- 
ditions and  records  for  the  sun  to  set  at  this 
point  on  his  course."  As  stated  above,  the 
writer  believes  this  to  be  the  true  explanation 
of  the  record  of  210  days  on  this  monument. 

In  figures  78  and  79  are  illustrated  the  Initial 
Series  and  Secondary  "Series  from  Stela  J  at 
Quirigua.^  For  lack  of  space  the  introducing 
glyph  in  this  text  has  been  omitted;  it  occupies 
the  position  of  six  glyph-blocks,  however, 
A1-B3,  after  which  the  Initial-series  number 
9.16.5.0.0  follows  in  A4-B8.  This  leads  to 
the  terminal  date  8  Ahau  8  Zotz,  which  is  re- 
corded in  A9,  B9,  Bl3,  the  glyph  in  Al3  being 
the  month-sign  indicator  here  shown  with  the 
coefficient  9.  Compare  B9  with  the  second  va- 
riant for  Ahau  in  figure  16  ¥,  i',  and  Bl3  with 
the  sign  for  Zotz  in  figure  19,  e,f.    The  Initial- 


FiG.  78.   The  Initial  Series  on 
Stela  J,  Quirigua. 


1  Since  the  Maya  New  Year's  day,  0  Pop,  always  fell  on  the  16th  of  July,  the  day  3  Yax  always  fell  on 
Jan.  15th,  at  the  commencement  of  the  dry  season. 

2  Since  0  Pop  fell  on  July  16th  (Old  Style),  18  Kayab  fell  on  June  19th,  which  is  very  near  the  summer 
solstice,  that  is,  the  seeming  northern  limit  of  the  sun,  and  roughly  coincident  with  the  begiiming  of  the 
rainy  season  at  Quirigua. 

3  For  the  full  text  of  this  inscription,  see  Maudslay,  1889-1902:  n,  pi.  46. 


216 


BUREAtJ  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


series  part  of  this  text  therefore  in  A1-B9,  Bl3,  is  perfectly  regular 
and  reads  as  follows:  9.16.5.0.0  8  Ahau  8  Zotz.  The  Secondary  Series, 
however,  are  unusual  and  differ  in  several  respects  from  the  ones 
heretofore  presented. 

The  first  Secondary  Series  inscribed  on  this  monument  (see  fig. 
79,  J.)  is  at  B1-B2.  This  series  the  student  should  readily  decipher 
as  3  kins,  13  uinals,  11  tuns,  and  0  katuns,  which  we  may  write 
0.11.13.3.  This  number  presents  one  feature,  which,  so  far  as  the 
writer  knows,  is  unique  in  the  whole  range  of  Maya  texts.  The  highest 
order  of  units  actually  involved  in  this  number  is  the  tun,  but  for 
some  unknown  reason  the  ancient  scribe  saw  fit  to  add  the  katun 

sign  also,  B2,  which,  how- 
ever, he  proceeded  to  nul- 
lify at  once  by  attaching 
to  it  the  coefficient  0.  For 
in  so  far  as  the  numerical 
value  is  concerned,  11.13.3 
and  0.11.13.3  are  equal. 
The  next  peculiarity  is 
that  the  date  which  fol- 
lows this  number  in  B3-A4 
is  not  its  terminal  date,  as 
we  have  every  reason  to 
expect,  but,  on  the  con- 
trary, its  starting  point. 

Fig.  79.   The  Secondary  Series  on  Stela  J,  Quirigua.  othcr   WOrds    in  this 

Secondary  Series  the  startuig  point  follows  instead  of  precedes  the 
number  counted  from  it.  This  date  is  very  clearly  12  Caban  6  Kayab ; 
compare  B3  with  the  sign  for  Caban  in  figure  16,  a',  V,  and  A4  with 
the  sign  for  Kayab  in  figure  19,  d'-f.  So  far  as  Stela  J  is  concerned 
there  is  no  record  of  the  position  which  this  date  occupied  in  the  Long 
Coimt;  that  is,  there  are  no  data  by  means  of  which  its  Initial  Series 
may  be  calculated.  Elsewhere  at  Quirigua,  however,  this  date  is  re- 
corded twice  as  an  Initial  Series  and  in  each  place  it  has  the  same 
value,  9.14.13.4.17.  We  may  safely  conclude,  therefore,  that  the  date 
in  A3-B4  is  9.14.13.4.17  12  Caban  5  Kayab,  and  use  it  in  our  cal- 
culations as  such.  Reducmg  0.11.13.3  to  units  of  the  first  order,  we 
have : 

B2=  0X7,  200  =  0 
A2  =  11X  360  =3,960 
Bl  =  13X  20  =  260 
Bl=  3X        1  =  3 


4,  223 


MOELET]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  217 

Applying  rules  1,  2,  and  3  (pp.  139,  140,  and  141,  respectively)  to  this 
number,  the  terminal  date  reached  will  be  10  Ahau  8  Chen,  which  is 
nowhere  recorded  in  the  text  (see  fig.  79,  A). 

The  Initial  Series  corresponding  to  this  date,  however,  may  bo 
calculated  from  the  Initial  Series  which  we  have  assigned  to  the  (hito 
12  Caban  5  Kayab : 

9.14.13.  4.17    12  Caban  5  Kayab 

0.11.13.  3 
9.15.  5.  0.  0    10  Ahau   8  Chen 

Although  the  date  9.15.5.0.0  10  Ahau  8  Chen  is  not  actually  recorded 
at  Quirigua,  it  is  reached  on  another  monument  by  calculation  just 
as  here.  It  has  a  peculiar  fitness  here  on  Stela  J  in  that  it  is  just 
one  katun  earlier  than  the  Initial  Series  on  this  monument  (see  fig. 
78),  9.16.5.0.0  8  Ahau  8  Zotz. 

The  other  Secondary  Series  on  this  monument  (see  fig.  79,  B) 
appears  at  B1-A2,  and  records  18  tuns,  3  uinals,  and  14  kins,  which 
we  may  write  thus:  18.3.14.  As  in  the  preceding  case,  the  date 
following  this  number  in  B2-A3  is  its  starting  point,  not  its  terminal 
date,  a  very  unusual  feature,  as  has  been  explained.  This  date  is 
6  Cimi  4  Tzec — compare  B2  with  the  sign  for  Cimi  in  figure  16,  h,  i, 
and  A3  with  the  sign  for  Tzec  in  figure  19,  p',  li — and  as  far  as  Stela  J 
is  concerned  it  is  not  fixed  in  the  Long  Count.  However,  elsewhere 
at  Quirigua  this  date  is  recorded  in  a  Secondary  Series,  which  is 
referred  back  to  an  Initial  Series,  and  from  this  passage  its  corre- 
sponding Initial  Series  is  found  to  be  9.15.6.14.6  6  Cimi  4  Tzec. 
Reducing 'the  number  recorded  in  B1-A2,  18.3.14,  to  imits  of  the 
first  order,  we  have: 

A2  =  18X360  =  6,  480 
B2=  3X  20=  60 
B2  =  14  X    1  =  14 


6,  554 

Applying  rules  1,  2,  and  3  (pp.  139,  140,  and  141,  respectively)  to  the 
number,  the  terminal  date  reached  will  be  8  Ahau  8  Zotz,  which  does 
not  appear  in  figure  79,  B.  The  Initial  Series  corresponding  to  this 
date  may  be  calculated  as  follows : 

9.15.  6.14.  6  6  Cimi  4  Tzec 
18.  3.14 

9.16.  5.  0.  0  8  Ahau  8  Zotz 

But  this  was  the  Initial  Series  recorded  on  the  reverse  of  this  monu- 
ment, consequently  the  Secondary-series  dates,  both  of  which  have  pre- 


218 


BUREAU  OF  AMEEICAN  ETHKOLOGY 


[bull.  57 


ceded  the  Initial-series  date  in  point  of  time,  bring  this  count  up  to 
the  contemporaneous  time  of  this  monument,  which  was  9.16.5.0.0 
8  Ahau  8  Zotz.  In  view  of  the  fact  that  the  Secondary  Series  on 
Stela  J  are  both  earher  than  the  Initial  Series,  the  chronological 
sequence  of  the  several  dates  is  better  preserved  by  regarding  the 
Initial  Series  as  being  at  the  close  of  the  inscription  instead  of  at  the 
beginning,  thus: 

9.14.13.  4.17    12  Caban  5  Kayab  Figure  79,  A,  B3-A4 

0.11.13.  3  B1-B2 
[9.15.  5.  0.  0]  [10  Ahau   8  Chen]  ^ 
[1.14.  6]  2 

9.15.  6.14.  6       6  Cimi  4  Tzec  Figure  79,  B,  B2-A3 
18.  3.14  B1-A2 

9.16.  5.  0.  0       8  Ahau  8  Zotz  Figure  78,     A1-B9,  Bl3 

By  the  above  arrangement  all  the  dates  present  in  the  text  lead  up 
to  9.16.5.0.0  8  Ahau  8  Zotz  as  the  most  important  date,  because  it 
alone  records  the  particular  hotun-ending  which  Stela  J  marks.  The 
importance  of  this  date  over  the  others  is  further  emphasized  by  the 
fact  that  it  alone  appears  as  an  Initial  Series. 

The  text  of  Stela  J  illustrates  two  points  in  connection  with  Sec- 
ondary Series  which  the  student  will  do  well  to  bear  in  mind:  (1) 
The  starting  points  of  Secondary-series  numbers  do  not  always  pre- 
cede the  numbers  counted  from  them,  and  (2)  the  terminal  dates  and 
starting  points  are  not  always  both  recorded. 

The  former  point  will  be  illustrated  in  the  following  example: 
In  plate  19,  J.,  is  figured  the  Initial  Series  from  the  west  side  of  Stela 
F  at  Quirigua.^  The  introducing  glyph  appears  in  A1-B2  and  is 
followed  by  the  Initial-series  number  in  A3-A5.  This  is  expressed 
by  head  variants  and  reads  as  follows:  9.14.13.4.17.  The  terminal 
date  reached  by  this  number  is  12  Caban  5  Kayab,  which  is  recorded 
in  B5-A6.  The  student  will  readily  identify  the  numerals  as  above 
by  comparing  them  with  the  forms  in  figures  51-53,  and  the  day  and 
month  signs  by  comparing  them  with  figures  16,  a\  h',  and  19,  d'-f, 
respectively.    The  Initial  Series  therefore  reads  9.14.13.4.17  12  Caban 

5  Kayab.* 

1  Bracketed  dates  are  those  which  are  not  actually  recorded  but  which  are  reached  by  numbers  appearing 
in  the  text. 

2  Although  not  recorded,  the  number  1.14.6  is  the  distance  from  the  date  9.15.5.0.0  reached  by  the  Second- 
ary Series  on  one  side  to  the  starting  point  of  the  Secondary  Series  on  the  other  side,  that  is,  9.15.6.14.6 

6  Cimi  4  Tzec. 

3  For  the  full  text  of  this  inscription  see  Maudslay,  1889-1902:  ii,  pis.  37,  39,  40.  For  convenience  in 
figuring,  the  lower  parts  of  columns  A  and  B  are  shown  in  B  instead  of  below  the  upper  part.  The 
numeration  of  the  gl5T)h-blocks,  however,  follows  the  arrangement  in  the  original. 

4  This  is  one  of  the  two  Initial  Series  which  justified  the  assumptions  made  in  the  previous  text  that 
the  date  12  Caban  5  Kayab,  which  was  recorded  there,  had  the  Initial-series  value  9.14.13.4.17,  as  here. 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57    PLATE  19 


INITIAL  SERIES  U)  AND  SECONDARY  SERIES  {B)   ON   STELA   F  (Vy/EST 

SIDE),  QUIRIGUA 


MOKLET]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  219 

Passing  over  B6-A10,  the  meanings  of  which  are  unknown,  we 
reach  in  BlO  the  Secondary-series  number  13.9.9.  Reducing  this  to 
units  of  the  first  order,  we  have: 

B6b  =  13X360  =4,  680 
B6a=  9X  20=  180 
B6a=  9X    1=  9 

4,  869 

Assuming  that  our  starting  point  is  the  date  next  preceding  this 
number  in  the  text,  that  is,  the  Initial-series  terminal  date  12  Caban 
5  Kayab  in  B5-A6,  and  applying  rules  1,  2,  and  3  (pp.  139,  140,  and 
141,  respectively),  the  terminal  day  reached  will  be  6  Cimi  4  Tzec. 
This  date  the  student  will  find  recorded  in  plate  19,  B,  Bllb-Al2a. 
Compare  Bllb  with  the  sign  for  Cimi  in  figure  16,  li,  i,  and  Al2a  with 
the  sign  for  Tzec  in  figure  19,  g,  7i.  Moreover,  since  the  Initial-series 
value  of  the  starting  point  12  Caban  5  Kayab  is  known,  the  Initial- 
series  value  of  the  terminal  date  6  Cimi  4  Tzec  may  be  calculated 
from  it : 

9.14.13.  4.17    12  Caban  5  Kayab 

13.  9.  9 
9.15.  6.14.  6    6  Cimi  4  Tzec  ^ 

In  Al5  is  recorded  the  date  3  Ahau  3  Mol  (compare  Al5a  with  fig.  16, 
Ji^,  i' ,  and  Al5b  with  fig.  19,  m,  n)  and  in  Al7  the  date  4  Ahau  13  Yax 
(compare  Al7a  with  fig.  16,  e'-g'  and  Al7b  with  fig.  19,  g,  r).  This 
latter  date,  4  Ahau  13  Yax,  is  recorded  elsewhere  at  Quirigua  in  a 
Secondary  Series  attached  to  an  Initial  Series,  where  it  has  the  Initial- 
series  value  9.15.0.0.0.  This  value  we  may  assume,  therefore,  belongs 
to  it  in  the  present  case,  giving  us  the  full  date  9.15.0.0.0  4  Ahau  13 
Yax.  For  the  present  let  us  pass  over  the  first  of  these  two  dates, 
namely,  3  Ahau  3  Mol,  the  Initial  Series  of  which  as  well  as  the  reason 
for  its  record  here  will  better  appear  later. 

In  Bl7-Al8a  is  recorded  ano.ther  Secondary-series  number  com- 
posed of  3  kins,  13  uinals,  16  tuns,  and  1  katun,  which  we  may  write 
thus:  1.16.13.3.  The  student  will  note  that  the  katun  coefficient  in 
Al8a  is  expressed  by  an  unusual  form,  the  thumb.  As  explained  on 
page  103,  this  has  a  numerical  value  of  1.  Again,  our  text  presents 
another  irregular  feature.  Instead  of  being  counted  either  forward 
or  backward  from  the  date  next  preceding  it  in  the  text;  that  is, 
4  Ahau  13  Yax  in  A17,  this  number  is  counted  from  the  date  following 
it  in  the  text,  like  the  two  Secondary-series  numbers  in  Stela  J,  just 
discussed.  This  starting  date  recorded  in  Al8b  Bl8a  is  12  Caban  5 
Kayab,  which,  as  we  have  seen,  is  also  the  date  recorded  by  the 
Initial  Series  in  plate  19,  A,  A1-A6.    We  are  perfectly  justified  in 


1  This  is  the  text  in  which  the  Initial-series  value  9.15.6.14.6  was  found  attached  to  the  date  6  Cimi  4  Tzec. 


220 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


assuming,  therefore,  that  the  12  Caban  5  Kayab  in  Al8b-Bl8a  had 
the  same  Initial-series  value  as  the  12  Caban  5  Kayab  in  plate  19,  A, 
B5-A6,  namely,  9.14.13.4.17.  Reducing  the  number  in  Bl7-Al8a, 
namely,  1.16.13.3,  to  units  of  the  first  order,  we  have: 

Al8a=  1  X7,200=  7,200 

Bl7b  =  16x    360=  5,760 

Bl7a  =  13X      20=  260 

Bl7a=  3X        1=  3 

13,223 

Remembering  that  this  number  is  to  be  counted  forward  from  the 
date  12  Caban  6  Kayab,  and  applying  rules  1,  2,  and  3  (pp.  139,  140, 
and  141,  respectively),  the  terminal  date  reached  will  be  1  Ahan  3 
Zip,  which  is  recorded  in  Al9.  Compare  the  coefficient  of  the  day 
sign  in  Al9a  with  the  coefficient  of  the  katun  sign  in  Al8a,  and  the 
day  sign  itself  with  the  profile  variant  for  Ahau  in  figure  16,  Ji^,  i\ 
For  the  month  sign,  compare  Al9b  with  figure  19,  d.  But  since  the 
Initial-series  value  of  the  starting  point  is  known,  we  may  calculate 
from  it  the  Initial-series  value  of  the  new  terminal  date: 

9.14.13.  4.17    12  Caban  6  Kayab 

1.16.13.  3 
9.16.10.  0.  0    1  AbailS  Zip 

Passing  over  to  the  east  side  of  this  monument,  the  student  will  find 
recorded  there  the  continuation  of  this  inscription  (see  pi.  20).^  This 
side,  like  the  other,  opens  with  an  introducing  glyph  A1-B2,  which 
is  followed  by  an  Initial  Series  in  A3-A5.  Although  this  number  is 
expressed  by  head  variants,  the  forms  are  all  familiar,  and  the  student 
will  have  little  difficulty  in  reading  it  as  9.16.10.0.0.  The  terminal 
date  which  this  number  reaches  is  recorded  in  B5-B8;  that  is,  P  Ahau 
3  Zip,  the  month  indicator"  appearing  as  a  head  variant  in  A8  with 
the  head-variant  coefficient  10.  But  this  date  is  identical  with  the 
date  determined  by  calculation  and  actually  recorded  at  the  close  of 
the  inscription  on  the  other  side  of  this  monument,  and  since  no  later 
date  is  recorded  elsewhere  in  this  text,  we  may  conclude  that 
9.16.10.0.0  1  Ahau  3  Zip  represents  the  contemporaneous  time  of 
Stela  F,  and  hence  that  it  was  a  regular  hotun-marker.  Here  again, 
as  in  the  case  of  Stela  J  at  Quirigua,  the  importance  of  the  '^contem- 
poraneous date"  is  emphasized  not  only  by  the  fact  that  all  the  other 
dates  lead  up  to  it,  but  also  by  the  fact  that  it  is  expressed  as  an 
Initial  Series. 

1  For  the  full  text  of  this  inscription  see  Maudslay,  1889-1902:  n,  pis.  38.  40. 

2  The  frontlet  seems  to  be  composed  of  but  one  element,  indicating  for  this  head  the  value  8  instead 
of  1.  However,  as  the  calculations  point  to  1,  it  is  probable  there  was  originally  another  element  to  the 
frontlet. 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57    PLATE  20 


NITIAL  SERIES  ON   STELA   F   (EAST  SIDE),  QUIRIGUA 


MOELEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


221 


We  have  explained  all  the  dates  figured  except  3  Ahau  3  Mol  in 
plate  19,  B,  Al5,  the  discussion  of  which  was  deferred  until  after  the 
rest  of  the  inscription  had  been  considered.    It  will  be  remembered 
in  connection  with  Stela  J  (figs.  78,  79)  that  one  of  the  dates  reached 
in  the  course  of  the  calculations  was  just  1  katun  earlier  than  the 
date  recorded  by  the  Initial  Series  on  the  same  monument.  Now, 
one  of  the  Initial-series  values  corresponding  to  the  date  3  Ahau  3 
Mol  here  under  discussion  is  9.15.10.0.0,  exactly  1  katun  earlier  than 
the  Initial-series  date  on  Stela 
F.    In  other  words,  if  we  give 
to  the  date  3  Ahau  3  Mol  in  A15 
the  value  9.15.10.0.0,  the  cases 
are  exactly  parallel.    While  it 
is  impossible  to  prove  that  this 
particular  Initial  Series  was  the 
one  which  the  ancient  scribes 
had   in  mind  when  they  re- 
corded this  date  3  Ahau  3  Mol, 
the  writer  believes  that  the  coincidence  and  parallel  here  presented  are 
sufiicient  to  warrant  the  assumption  that  this  is  the  case.    The  whole 
text  reads  as  follows: 


a 


Fig.  80. 


Glyphs  which  may  disclose  the  nature  of  the 
events  that  happened  at  Quirigua  on  the  dates: 
a,  9.  14.  13.  4. 17  12  Caban  5  Kayab;  h,  9.  15.  6. 14.  G 
6  Cimi  4  Tzec. 


9.14.13 

13.  9. 
9.15.  6.14. 
[9.15.10.  0. 
[9.15.  0.  0. 
9.14'.13.  4. 
1.16.13. 


4.17 
9.  9 


6 
0] 
0] 
17 
3 


12  Caban  5  Kayab 

6  Cimi  4  Tzec 

3  Ahau  3  Mol 

4  Ahau  13  Yax 
12  Caban  5  Kayab 


9.16.10.  0.  0 


Plate  19,  A,  A1-A6 
Plate  19,  .4,  AlO 
Plate  19,  B,  Bllb-Al2a 
Plate  19,  B,  Al5 
Plate  19,  B,  A17 
Plate  19,  B,  Al8b  Bl8a 
Plate  19,  B,  Bl7  Al8a 
Plate  19,  B,  Al9 


1  Ahau  3  Zip 

(repeated  as  Initial  Series  on  east  side  of  monument) 
9.16.10.  0.  0        1  Ahau  3  Zip         Plate  20,  A1-B5-B8 

The  student  will  note  the  close  similarity  between  this  inscription  and 
that  on  Stela  J  (figured  in  figs.  78  and  79),  a  summary  of  which  appears 
on  page  239.  Both  commence  with  the  same  date,  9.14.13.4.17  12 
Caban  5  Kayab;  both  show  the  date  9.15.6.14.6  6  Cimi  4  Tzec;  both 
have  dates  which  are  just  1  katun  in  advance  of  the  ho  tuns  which 
they  mark;  and  finally,  both  are  ho  tun-markers.  Stela  J  preceding 
Stela  F  by  just  1  hotun.  The  date  from  which  both  proceed, 
9.14.13.4.17  12  Caban  5  Kayab,  is  an  important  one  at  Quirigua, 
being  the  earliest  date  there.  It  appears  on  four  monuments,  namely, 
Stelse  J,  F,  and  E,  and  Zoomorph  G.  Although  the  writer  has  not 
been  able  to  prove  the  point,  he  is  of  the  opinion  that  the  glyph 
shown  in  figure  80,  a,  tells  the  meaning  of  the  event  which  happened 
on  this  date,  which  is,  moreover,  the  earliest  date  at  Quirigua  which 


222 


BUREAU  OF  AMEEICAN  ETHNOLOGY 


[bull.  57 


it  is  possible  to  regard  as  being  contemporaneous.  Hence,  it  is  not 
improbable  that  it  might  refer  to  the  founding  of  the  city  or  some 
similar  event,  though  this  is  of  course  a  matter  of  speculation.  The 
fact,  however,  that  9.14.13.4.17  12  Caban  5  Kayab  is  the  earliest 
date  on  four  different  hotun-markers  shows  that  it  was  of  supreme 
importance  in  the  history  of  Quirigua.  This  concludes  the  discus- 
sion of  texts  showing  the  use  of  Secondary  Series  with  Initial  Series. 

Texts  Kecording  Period  Endings 

It  was  explained  in  Chapter  III  (p.  77)  that  in  addition  to  Initial- 
series  dating  and  Secondary-series  dating,  the  Maya  used  still 
another  method  in  fixing  events,  which  was  designated  Period-ending 
dating.  It  was  explained  further  that,  although  Period-ending  dating 
was  less  exact  than  the  other  two  methods,  it  served  equally  well  for 
all  practical  purposes,  since  dates  fixed  by  it  could  not  recur  until 
after  a  lapse  of  more  than  18,000  years,  a  considerably  longer  period 
than  that  covered  by  the  recorded  history  of  mankind.  Finally,  the 
student  will  recall  that  the  katun  was  said  to  be  the  period  most 
commonly  used  in  this  method  of  dating. 

The  reason  for  this  is  near  at  hand.  Practically  all  of  the  great 
southern  cities  rose,  flourished,  and  fell  within  the  period  called  Cycle 
9  of  Maya  chronology.  There  could  have  been  no  doubt  throughout 
the  southern  area  which  particular  cycle  was  meant  when  the  ''cur- 
rent cycle"  was  spoken  of.  After  the  date  9.0.0.0.0  8  Ahau  13  Chen 
had  ushered  in  a  new  cycle  there  could  be  no  change  in  the  cycle 
coefficient  until  after  a  lapse  of  very  nearly  400  (394.250  +  )  years. 
Consequently,  after  Cycle  9  had  commenced  many  succeeding  gen- 
erations of  men  knew  no  other,  and  in  time  the  term  ''current  cycle" 
came  to  mean  as  much  on  a  monument  as  "Cycle  9."  Indeed,  in 
Period-ending  dating  the  Cycle  9  was  taken  for  granted  and 
scarcely  ever  recorded.  The  same  practice  obtains  very  generally 
to-day  in  regard  to  writing  the  current  century,  such  expressions  as 
July  4,  '12,  December  25,  '13,  being  frequently  seen  in  place  of  the 
full  forms  July  4,  1912,  A.  D.,  December  25,  1913,  A.  D.;  or  again, 
even  more  briefly,  7/4/12  and  12/25/13  to  express  the  same  dates, 
respectively.  The  desire  for  brevity,  as  has  been  explained,  prob- 
ably gave  rise  to  Period-ending  dating  in  the  first  place,  and  in  this 
method  the  cycle  was  the  first  period  to  be  eliminated  as  superfluous 
for  all  practical  purposes.  No  one  could  have  forgotten  the  number 
of  the  current  cycle. 

When  we  come  to  the  next  lower  period,  however,  the  katun,  we 
find  a  different  state  of  affairs.  The  numbers  belonging  to  this 
period  were  changing  every  20  (exactly,  19.71  +  )  years;  that  is,  three 
or  four  times  in  the  lifetime  of  many  individuals;  hence,  there  was 


BUREAU  OF  AMERICAN  ETHNOLOGY  BULLETIN  57    PLATE  21 


A     STELA  2,  COPAN  B.    TEMPLE  OF  THE  FOLIATED 

CROSS,  PALENQUE 


H.    STELA  C  (WEST  SIDE),  QUIRIGUA 

EXAMPLES  OF  PERIOD-ENDING  DATES  IN   CYCLE  9 


MOELEYj      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  223 

plenty  of  opportunity  for  confusion  about  the  number  of  the  katiiii 
in  which  a  particular  event  occurred.  Consequently,  in  ordov  to 
insure  accuracy  the  katun  is  almost  always  the  unit  used  in  Period- 
ending  dating. 

In  plate  21  are  figured  a  number  of  Period-ending  dates,  the  glyphs 
of  which  have  been  ranged  in  horizontal  lines,  and  are  numbered 
from  left  to  right  for  convenience  in  reference.  The  true  positions 
of  these  glyphs  in  the  texts  from  which  they  have  been  taken  are 
given  in  the  footnotes  in  each  case.  In  plate  21 ,  J.,  is  figured  a  Period- 
ending  date  from  Stela  2  at  Copan.^  The  date  12  Ahau  8  Cell  ap- 
pears very  clearly  in  glyphs  1  and  2.  Compare  the  month  sign  with 
figure  19,  u,  v.  There  follows  in  3  a  glyph  the  upper  part  of  which 
probably  represents  the  '^ending  sign"  of  this  date.  By  comparing 
this  form  with  the  ending  signs  in  figure  37  its  resemblance  to  figure 
37,  o,  will  be  evident.  Indeed,  figure  37,  o,  has  precisely  the  same 
lower  element  as  glyph  3.  In  glyph  4  follows  the  particular  katun, 
11,  whose  end  fell  on  the  date  recorded  in  glyphs  1  and  2.  The  stu- 
dent can  readily  prove  this  for  himself  by  reducing  the  Period-ending 
date  here  recorded  to  its  corresponding  Initial  Series  and  counting 
the  resulting  number  forward  from  the  common  starting  point,  4  Ahau 
8  Cumliu,  as  follows:  Since  the  cycle  glyph  is  not  expressed,  we  may 
fill  this  omission  as  the  Maya  themselves  filled  it,  by  supplying  Cycle 
9.  Moreover,  since  the  end  of  a  katun  is  recorded  here,  it  is  clear 
that  all  the  lower  periods — the  tuns,  uinals,  and  kins — will  have  to 
appear  with  the  coefiicient  0,  as  they  are  all  brought  to  their  respec- 
tive ends  with  the  ending  of  any  katun.  Therefore  we  may  write  the 
Initial-series  number  corresponding  to  the  end  of  Katun  11,  as 
9.11.0.0.0.  Treating  this  number  as  an  Initial  Series,  that  is,  first 
reducing  it  to  units  of  the  first  order,  then  deducting  from  it  all  the 
Calendar  Eounds  possible,  and  finally  applying  rules  1,  2,  and  3  (pp. 
139,  140,  and  141,  respectively)  to  the  remainder,  the  student  will  find 
that  the  terminal  date  reached  will  be  the  same  as  the  date  recorded 
in  glyphs  1  and  2,  namely,  12  Ahau  8  Ceh.  In  other  words,  the  Katun 
11,  which  ended  on  the  date  12  Ahau  8  Ceh,  was  9.11.0.0.0  12  Ahau 
8  Ceh,  and  both  indicate  exactly  the  same  position  in  the  Long 
Count.  The  next  example  (pi.  21,  B)  is  taken  from  the  tablet  in  the 
Temple  of  the  FoUated  Cross  at  Palenque.^  In  glyph  1  appears  the 
date  8  Ahau  8  TJo  (compare  the  month  form  with  fig.  19,  h,  c)  and  in 
glyph  3  the  ''ending"  of  Katun  13.  The  endmg  sign  here  is  the 
variant  shown  in  figure  37,  a-Ji,  and  it  occurs  just  above  the  coeffi- 
cient 13.  These  two  glyphs  therefore  record  the  fact  that  Katun  13 
ended  with  the  day  8  Ahau  8  TJo.  The  student  may  again  test  the 
accuracy  of  the  record  by  changing  this  Period-ending  date  to  its 

1  See  Maudslay,  1889-1902:  i,  pi.  102,  west  side,  glyphs  A5b-A7a. 

2  See  ibid.:  iv,  pi.  81,  glyphs  N15  015. 


224 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


corresponding  Initial-series  number,  9.13.0.0.0,  and  performing  the 
various  operations  indicated  in  such  cases.  The  resulting  Initial- 
series  terminal  date  will  be  the  same  as  the  date  recorded  in  glyphs  1 
and  2,  8  Ahau  8  Uo. 

In  plate  21,  (7,  is  figured  a  Period-ending  date  taken  from  Stela  23 
at  Naranjo.^  The  date  6  Ahau  13  Muan  appears  very  clearly  in  glyphs 
1  and  2  (compare  the  month  form  with  fig.  19,  a',  V).  Glyph  3  is 
the  ending  sign,  here  showing  three  common  ''ending  elements,"  (1) 
the  clasped  hand;  (2)  the  element  with  the  curl  infix;  (3)  the  tassel- 
like postfix.  Compare  this  form  with  the  ending  signs  in  figure  37, 
Z-^,  and  with  the  zero  signs  in  figure  54.  In  glyph  4  is  recorded  the 
particular  katun,  14,  which  came  to  its  end  on  the  date  recorded  in 
1  and  2.  The  element  prefixed  to  the  Katun  14  in  glyph  4  is  also 
an  ending  sign,  though  it  always  occurs  as  a  prefix  or  superfix  attached 
to  the  sign  of  the  period  whose  close  is  recorded.  Examples  illus- 
trating its  use  are  shown  in  figure  37,  a-h,  with  which  the  ending 
element  in  glyph  4  should  be  compared.  The  glyphs  1  to  4  in  plate 
21,  ^7,  therefore  record  that  Katun  14  came  to  an  end  on  the  date 
6  Ahau  13  Muan.  As  we  have  seen  above,  this  could  be  shown  to 
correspond  with  the  Initial  Series  9.14.0.0.0  6  Ahau  13  Muan. 

This  same  date,  6  Ahau  13  Muan  ending  Katun  14,  is  also  recorded 
on  Stela  16  at  Tikal  (see  pi.  21,  D)."^  The  date  itself  appears  in 
glyphs  1  and  2  and  is  followed  in  3  by  a  sign  which  is  almost  exactly 
like  the  ending  sign  in  glyph  3  just  discussed  (see  pi.  21,  C).  The 
subfixes  are  identical  in  both  cases,  and  it  is  possible  to  distinguish 
the  lines  of  the  hand  element  in  the  weathered  upper  part  of  the 
glyph  in  3.  Compare  glyph  3  with  the  ending  signs  in  figure  37,  Z-g-, 
and  with  the  zero  signs  in  figure  54.  As  in  the  preceding  example, 
glyph  4  shows  the  particular  katun  whose  end  is  recorded  here — Katun 
14.  The  period  glyph  itself  appears  as  a  head  variant  to  which  is 
prefixed  the  same  ending  prefix  or  superfix  shown  with  the  period 
glyph  in  the  preceding  example.  See  also  figure  37,  a-li.  As  above 
stated,  the  Initial  Series  corresponding  to  this  date  is  9.14.0.0.0  6 
Ahau  13  Muan. 

One  more  example  will  suffice  to  illustrate  the  use  of  katun  Period- 
ending  dates.  In  plate  21,  E,  is  figured  a  Period-ending  date  from 
Stela  4  at  Copan.^  In  glyphs  1  and  2  appears  the  date  4  Ahau  13-Yax 
(compare  the  month  m  glyph  2  with  fig.  19,  c[,  r),  which  is  followed 
by  the  ending  sign  in  3.  This  is  composed  of  the  hand,  a  very  com- 
m^on  ''ending"  element  (see  fig.  37,  j,  1)  with  a  grotesque  head  super- 
fix,  also  another  "ending  sign"  (see  i,  r,  u,  v  of  the  plate  just 
named).    In  glyph  4  follows  the  particular  katun  (Katun  15)  whose 

1  See  Maler,  1908  b:  iv,  No.  2,  pi.  38,  east  side,  glyphs  A17-B18. 

2  See  ibid.,  1911:  v,  pi.  26,  gljT^s  A1-A4. 

3  See  Maudslay,  1889-1902:  i,  pi.  104,  glyphs  A7,  B7. 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEKOGLYPHS 


225 


end  is  here  recorded.  This  date  corresponds  to  the  Initial  Series 
9.15.0.0.0  4  Ahau  13  Yax. 

Cases  where  tun  endings  are  recorded  are  exceedingly  rare. 
The  bare  statement  that  a  certain  tun,  as  Tun  10,  for  exampl(>,  had 
come  to  its  end  left  much  to  be  desired  in  the  way  of  accuracy,  since 
there  was  a  Tun  10  in  every  katun,  and  consequently  any  given  tun 
recurred  after  an  interval  of  20  years;  in  other  words,  there  were 
three  or  four  different  Tun  lO's  to  be  distinguished  from  one  another 
in  the  average  lifetime.  Indeed,  to  keep  them  apart  at  all  it  was 
necessary  either  to  add  the  particular  katun  in  which  each  fell  or  to 
add  the  date  on  which  each  closed.  The  former  was  a  step  away 
from  the  brevity  which  probably  prompted  the  use  of  Period-ending 
dating  in  the  first  place,  and  the  latter  imposed  too  great  a  task  on 
the  memory,  that  is,  keeping  in  mind  the  60  or  70  various  tun  end- 
ings which  the  average  lifetime  included.  For  these  reasons  tun- 
ending  dates  occur  but  rarely,  only  when  there  was  little  or  no  doubt 
concerning  the  particular  katun  in  which  they  fell. 

In  plate  21,  F,  is  figured  a  tun-ending  date  from  the  tablet  in  the 
Temple  of  the  Inscription  at  Palenque.^  In  glyph  1  appears  an  ending 
sign  showing  the  hand  element  and  the  grotesque  flattened  head  (for 
the  latter  see  fig.  37,  ^,  r,  u,  v),  both  common  ending  signs.  The 
remaining  element,  another  grotesque  head  with  a  flaring  postfix,  is 
an  unusual  variant  of  the  tun  head  found  only  at  Palenque  (see  fig. 
29,  7i).  The  presence  of  the  tun  sign  with  these  two  ending  signs 
indicates  probably  that  some  tun  ending  follows.  Glyphs  2  and  3 
record  the  date  5  Ahau  18  Tzec,  and  glyph  4  records  Tun  13.  We 
have  here  then  the  record  of  a  Tun  13,  which  ended  on  the  date 
5  Ahau  18  Tzec.  But  which  of  the  many  Tun  13s  in  the  Long  Count 
was  the  one  that  ended  on  this  particular  date  ?  To  begin  with,  we  are 
perfectly  justified  in  assuming  that  this  particular  tun  occurred  some- 
where in  Cycle  9,  but  this  assumption  does  not  aid  us  greatly,  since 
there  were  twenty  different  Tun  13s  in  Cycle  9,  one  for  each  of  the 
twenty  katuns.  However,  in  the  full  text  of  the  inscription  from 
which  this  example  is  taken,  5  Ahau  3  Chen  is  the  date  next  preceding, 
and  although  the  fact  is  not  recorded,  this  latter  date  closed  Katun  8 
of  Cycle  9.  Moreover,  shortly  after  the  tun-ending  date  here  under 
discussion,  the  date  ''3  Ahau  3  Zotz,  end  of  Katun  9,"  is  recorded.  It 
seems  likely,  therefore,  that  this  particular  Tun  13,  which  ended  on 
the  date  5  Ahau  18  Tzec,  was  9.8.13.0.0  of  the  Long  Count,  after 
9.8.0.0.0  but  before  9.9.0.0.0.  Reducing  this  number  to  units  of  the 
first  order,  and  appl3dng  the  several  rules  given  for  solving  Initial 
Series,  the  terminal  date  of  9.8.13.0.0  will  be  found  to  agree  with  the 
terminal  date  recorded  in  glyphs  2  and  3,  namely,  6  Ahau  18  Tzec, 

1  See  Maudslay,  1889-1902:  iv,  pi.  60,  glyplis  M1-N2. 
43508°— Bull.  57— 15  15 


226 


BUREAU  OF  AMEEICAN  ETHNOLOGY 


[bull.  57 


and  this  tun  ending  corresponded,  therefore,  to  the  Initial  Series 
9.8.13.0.0  6  Ahau  18  Tzec. 

Another  tun-ending  date  from  Stela  5  at  Tikal  is  figured  in  plate 
21,  G}  In  glyphs  1  and  2  the  date  4  Ahau  8  Yaxkin  appears,  the 
month  sign  being  represented  as  a  head  variant,  which  has  the  essen- 
tial elements  of  the  sign  for  Yaxkin  (see  fig.  19,  Ic,  I).  Following  this 
in  glyph  3  is  Tun  13,  to  which  is  prefixed  the  same  ending-sign 
variant  as  the  prefixial  or  superfixial  elements  in  figure  37,  i,  r,  u,  v. 
We  have  recorded  here  then  "Tun  13  ending  on  4  Ahau  8  Yaxkin," 
though  there  seems  to  be  no  mention  elsewhere  in  this  inscription 
of  the  number  of  the  katun  in  which  this  particular  tun  fell.  By 
referring  to  Great  Cycle  54  of  Goodman's  Tables  (Goodman,  1897), 
however,  it  appears  that  Tun  13  of  Katim  15  of  Cycle  9  closed  with 
this  date  4  Ahau  8  Yaxkin,  and  we  may  assume,  therefore,  that  this 
is  the  correct  position  in  the  Long  Count  of  the  tun-ending  date  here 
recorded.  This  date  corresponds  to  the  Initial  Series  9.15.13.0.0  4 
Ahau  8  Yaxkin. 

There  is  a  very  imusual  Period-ending  date  on  the  west  side  of 
Stela  C  at  Quirigua^  (see  pi.  21,  fl^).  In  glyphs  1  and  2  appears  the 
number  0  kins,  0  uinals,  5  tuns,  and  17  katuns,  which  we  may  write 
17.5.0.0,  and  following  this  in  glyphs  3  and  4  is  the  date  6  Ahau  13 
Kayab.  At  first  sight  this  would  appear  to  be  a  Secondary  Series, 
the  number  17.5.0.0  being  counted  forward  from  some  preceding 
date  to  reach  the  date  6  Ahau  13  Kayab  recorded  just  after  it.  The 
next  date  preceding  this  on  the  west  side  of  Stela  C  at  Quirigua  is  the 
Initial-series  terminal  date  6  Ahau  13  Yaxkin,  illustrated  together  with 
its  corresponding  Initial-series  number  in  figure  68,  A.  However, 
all  attempts  to  reach  the  date  6  Ahau  13  Kayab  by  counting  either 
forward  or  backward  the  number  17.5.0.0  from  the  date  6  Ahau  13 
Yaxkin  will  prove  unsuccessful,  and  we  must  seek  another  explana- 
tion for  the  four  glyphs  here  under  discussion.  If  this  were  a  Period- 
ending  date  it  would  mean  that  Tun  5  of  Katun  17  came  to  an  end 
on  the  date  6  Ahau  13  Kayab.  Let  us  see  whether  this  is  true. 
Assuming  that  our  cycle  coefficient  is  9,  as  we  have  done  in  all  the 
other  Period-ending  dates  presented,  we  may  express  glyphs  1  and  2 
as  the  following  Initial-series  number,  provided  they  represent  a 
period  ending,  not  a  Secondary-series  number:  9.17.5.0.0.  Reduc- 
ing this  number  to  units  of  the  1st  order,  and  applying  the  rules 
previously  given  for  solvmg  Initial  Series,  the  terminal  date  reached 
will  be  6  Ahau  13  Kayab,  identical  with  the  date  recorded  in  glyphs 
3  and  4.  We  may  conclude,  therefore,  that  this  example  records  the 
fact  that  ''Tun  5  of  Katun  17  ended  on  the  date  6  Ahau  13  Kayab," 
this  being  identical  with  the  Initial  Series  9.17.5.0.0  6  Ahau  13  Kayab. 


1  Maler,  1911:  v,  pi.  17,  east  side,  glyphs  A4-A5. 

2  See  Maudslay,  1889-1902:  ii,  pi.  19,  west  side,  glyphs  B10-A12. 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57    PLATE  22 


A.    CYCLE  13:  TEMPLE  OF  THE  CROSS,  PALENQUE 


0® 


B.    CYCLE  13:    ROUND  ALTAR,  PIEDRAS  NEGRAS 


a    CYCLE  2:  TEMPLE  OF  THE  FOLIATED  CROSS,  PALENQUE 


O    O  OOP 


i).    CYCLE  10:  STELA  11,  SEIBAL 


E.    CYCLE  10:  STELA  8,  COPAN 


F.    CYCLE  10:  ZOOMORPH  G,  QUIRIGUA 


O^op  0 

'  '  0 

0 


O.    CYCLE  8:    TEMPLE  OF  THE  CROSS,  PALENQUE 

EXAMPLES  OF  PERIOD-ENDING  DATES  IN  CYCLES  OTHER  THAN  CYCLE  9 


MOELEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  227 

The  foregoing  Period-ending  dates  have  all  been  in  Cycle  9,  even 
though  this  fact  has  not  been  recorded  in  any  of  the  above  examples. 
We  come  next  to  the  consideration  of  Period-ending  dates  which 
occurred  in  cycles  other  than  Cycle  9. 

In  plate  22,  A,  is  figured  a  Period-ending  date  from  the  tablet  in 
the  Temple  of  the  Cross  at  Palenque.^  In  glyphs  1  and  2  appejirs 
the  date  4  Ahau  8  Cumliu  (compare  the  month  form  in  glyph  2  with 
fig.  19,  g',  li')-,  and  in  glyph  3  an  ending  sign  (compare  glyph  3  with 
the  ending  signs  in  fig.  37,  Z-g,  and  with  the  zero  signs  in  fig.  54). 
There  follows  in  glyph  4,  Cycle  13.  These  four  glyphs  record  the  fact, 
therefore,  that  Cycle  13  closed  on  the  date  4  Ahau  8  Cumliu,  the  start- 
ing point  of  Maya  chronology.  This  same  date  is  again  recorded  on 
a  round  altar  at  Piedras  Negras  (see  pi.  22,  B)?  In  glyphs  1  and  2 
appears  the  date  4  Ahau  8  Cumhu,  and  in  glyph  3a  the  ending  sign, 
which  is  identical  with  the  ending  sign  in  the  preceding  example, 
both  having  the  clasped  hand,  the  subfix  showing  a  curl  infix,  and 
the  tassel-like  postfix.  Compare  also  figure  37,  l-q^,  and  figure  54. 
Glyph  3b  clearly  records  Cycle  13.  The  dates  in  plate  22,  A,  B,  are 
therefore  identical.  In  both  cases  the  cycle  is  expressed  by  its 
normal  form. 

In  plate  22,  C,  is  figured  a  Period-ending  date  from  the  tablet  in  the 
Temple  of  the  Fohated  Cross  at  Palenque.^  In  glyph  1  appears  an 
ending  sign  in  which  the  hand  element  and  tassel-like  postfix  show 
clearly.  This  is  followed  in  glyph  2  by  Cycle  2,  the  clasped  hand  on 
the  head  variant  unmistakably  indicating  the  cycle  head.  Finally, 
in  glyphs  3  and  4  appears  the  date  2  Ahau  3  Uayeb  (compare  the 
month  form  with  fig.  19,  i')  The  glyphs  in  plate  22,  C,  record,  there- 
fore, the  fact  that  Cycle  2  closed  on  the  date  2  Ahau  3  XJayeb,  a  fact 
which  the  student  may  prove  for  himself  by  converting  this  Period- 
ending  date  into  its  corresponding  Initial  Series  and  solving  the  same. 
Since  the  end  of  a  cycle  is  recorded  here,  it  is  evident  that  the  katun, 
tun,  uinal,  and  kin  coefiicients  must  all  be  0,  and  our  Initial-series 
number  will  be,  therefore,  2.0.0.0.0.  Reducing  this  to  units  of  the 
1st  order  and  proceeding  as  in  the  case  of  Initial  Series,  the  terminal 
date  reached  will  be  2  Ahau  3  Uayeb,  just  as  recorded  in  glyphs  3 
and  4.  The  Initial  Series  corresponding  to  this  Period-ending  date 
will  be  2.0.0.0.0  2  Ahau  3  Uayeb. 

These  three  Period-ending  dates  (pi.  22,  A-C)  are  not  to  be  consid- 
ered as  referring  to  times  contemporaneous  with  the  erection  of  the 
monuments  upon  which  they  are  severally  inscribed,  since  they  pre- 

1  See  Maudslay,  1889-1902:  iv,  pi.  75,  glyphs  D3-C5. 

2  See  Maler,  1901:  ii,  No.  1,  pi.  8,  glyphs  A1-A2. 
8  See  Maudslay,  op.  cit.,  pi.  81,  glyphs  C7-D8. 

4  It  will  be  remembered  that  ITayeb  was  the  name  for  the  xma  kaba  kin,  the  5  closing  days  of  the  year. 
Dates  which  fall  in  this  period  are  exceedingly  rare,  and  in  the  inscriptions,  so  far  as  the  writer  knows, 
have  been  found  only  at  Palenque  and  Tikal. 


228 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


cede  the  opening  of  Cycle  9,  the  first  historic  epoch  of  the  Maya  civ- 
ihzation,  by  periods  ranging  from  2,700  to  3,500  years.  As  explained 
elsewhere,  they  probably  referred  to  mythological  events.  There  is 
a  date,  however,  on  a  tablet  in  the  Temple  of  the  Cross  at  Palenque 
which  falls  in  Cycle  8,  being  fixed  therein  by  an  adjoining  Period- 
ending  date  that  may  have  been  historical.  This  case  is  figured  in 
plate  22,  G}  In  glyphs  4  and  5  appears  the  date  8  Ahau  13  Cell 
(compare  the  month  form  in  glyph  5  with  fig.  16,  u,  v).  This  is  fol- 
lowed in  glyph  6  by  a  sign  which  shows  the  same  ending  element  as 
the  forms  in  figure  37,  i,  r,  u,  v,  and  this  in  turn  is  followed  by  Cycle 

9  in  glyph  7.  The  date  recorded  in  this  case  is  Cycle  9  ending  on  the 
date  8  Ahau  13  Ceh,  which  corresponds  to  the  Initial  Series  9.0.0.0.0 
8  Ahau  13  Ceh. 

Now,  in  glyphs  1  and  2  is  recorded  the  date  2  Caban  10  Xul  (com- 
pare the  day  sign  with  fig.  16,  a',  6',  and  the  month  sign  with  fig. 
19,  i,  j),  and  following  this  date  in  glyph  3  is  the  number  3  kins,  6 
uinals,  or  6.3.  This  looks  so  much  like  a  Secondary  Series  that  we 
are  justified  in  treating  it  as  such  until  it  proves  to  be  otherwise.  As 
the  record  stands,  it  seems  probable  that  if  we  count  this  number 
6.3  in  glyph  3  forward  from  the  date  2  Caban  10  Xul  in  glyphs  1  and 
2,  the  terminal  date  reached  will  be  the  date  recorded  in  glyphs  4 
and  5;  that  is,  the  next  date  following  the  number.  Reducing  6.3 
to  units  of  the  first  order,  we  have: 

Glyph  6  =  6X20  =  120 
Glyph  6  =  3  X  1=  3 

123 

Counting  this  number  forward  from  2  Caban  10  Xul  according  to  the 
rules  which  apply  in  such  cases,  the  terminal  day  reached  will  be 
8  Ahau  13  Ceh,  exactly  the  date  which  is  recorded  in  glyphs  4  and  5. 
But  this  latter  date,  we  have  just  seen,  is  declared  by  the  text  to  have 
closed  C>cle  9,  and  therefore  corresponded  with  the  Initial  Series 
9.0.0.0.0  8  Ahau  13  Ceh.  Hence,  from  this  known  Initial  Series  we 
may  calculate  the  Initial  Series  of  the  date  2  Caban  10  Xul  by  sub- 
tracting from  9.0.0.0.0  the  number  6.3,  by  which  the  date  2  Caban 

10  Xul  precedes  the  date  9.0.0.0.0  8  Ahau  13  Ceh: 

9.  0.  0.  0.  0    8  Ahau  13  Ceh 

6.  3 

8.19.19.11.17    2  Caban  10  Xul 

This  latter  date  fell  in  Cycle  8,  as  its  Initial  Series  indicates.  It  is 
quite  possible,  as  stated  above,  that  this  date  may  have  referred  to 
some  actual  historic  event  in  the  annals  of  Palenque,  or  at  least  of 


1  See  Maudslay,  1889-1902:  iv,  pi.  77,  glyphs  P14-R2.  Glyphs  Q15-P17  are  omitted  from  pi.  22,  G,  as 
they  appear  to  be  uncalendrical. 


MOELEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  229 


the  southern  Maya,  though  the  monument  upon  which  it  is  recorchul 
probably  dates  from  an  epoch  at  least  200  years  later. 

In  a  few  cases  Cycle-10  ending  dates  have  been  found.  Some  of 
these  are  surely  '^contemporaneous,"  that  is,  the  monuments  upon 
which  they  appear  really  date  from  Cycle  10,  while  others  are  as 
surely  prophetic,"  that  is,  the  monuments  upon  which  they  are 
found  antedate  Cycle  10.  Examples  of  both  kinds  follow. 
,  In  plate  22,  E,  is  figured  a  Period-ending  date  from  Stela  8  at  Copan.^ 
Glyphs  1  and  2  declare  the  date  7  Ahau  18  ?,  the  month  sign  in  glyph 
2  being  effaced.  In  glyph  3  is  recorded  Cycle  10,  the  cycle  sign  being 
expressed  by  its  corresponding  head  variant.  Note  the  clasped  hand, 
the  essential  characteristic  of  the  cycle  head.  Above  this  appears  the 
same  endingsign  as  that  shown  in  figure  37,  a-h,  and  it  would  seem  prob- 
able, therefore,  that  these  three  glyphs  record  the  end  of  Cycle  10. 
Let  us  test  this  by  changing  the  Period-ending  date  in  glyph  3  into 
its  corresponding  Initial-series  number  and  then  solving  this  for  the 
resulting  terminal  date.  Since  the  end  of  a  cycle  is  here  indicated, 
the  katim,  tun,  uinal,  and  kin  coefiicients  must  be  0  and  the  Initial- 
series  number  will  be,  therefore,  10.0.0.0.0.  Reducing  this  to  units 
of  the  first  order  and  applying  the  rules  indicated  in  such  cases,  the 
resulting  terminal  date  will  be  found  to  be  7  Ahau  18  Zip.  But  this 
agrees  exactly  with  the  date  recorded  in  glyphs  1  and  2  so  far  as  the 
latter  go,  and  since  the  two  agree  so  far  as  they  go,  we  may  conclude 
that  glyphs  1-3  in  plate  22,  E,  express  ''Cycle  10  ending  on  the  date 
7  Ahau  18  Zip."  Although  this  is  a  comparatively  late  date  for 
Copan,  the  writer  is  inclined  to  believe  that  it  was  "contemporane- 
ous" rather  than  "prophetic." 

The  same  can  not  be  said,  however,  for  the  Cycle-10  ending  date 
on  Zoomorph  G  at  Quirigua  (see  pi.  22,  F).  Indeed,  this  date,  as  will 
appear  below,  is  almost  surely  "prophetic"  in  character.  Glyphs  1 
and  2  record  the  date  7  Ahau  18  Zip  (compare  the  month  form  in  glyph 
2  with  fig.  19,  d)  and  glyph  3  shows  very  clearly  "  the  end  of  Cycle 
10."  Compare  the  ending  prefix  in  glyph  4  with  the  same  element 
in  fig.  37,  a-h.  Hence  we  have  recorded  here  the  fact  that  "Cycle 
10  ended  on  the  date  7  Ahau  18  Zip,"  a  fact  proved  also  by  calcula- 
tion in  connection  with  the  preceding  example.  Does  this  date  rep- 
resent, therefore,  the  contemporaneous  time  of  Zoomorph  G,  the  time 
at  which  it  was  erected,  or  at  least  dedicated?  Before  answering 
this  question,  let  us  consider  the  rest  of  the  text  from  which  this 
example  is  taken.  The  Initial  Series  on  Zoomorph  G  at  Quirigua  has 
already  been  shown  in  figure  70,  and,  according  to  page  187,  it  records 
the  date  9.17.15.0.0  5  Ahau  3  Muan.  On  the  grounds  of  antecedent 
probabihty,  we  are  justified  in  assuming  at  the  outset  that  this  date 


1  See  Maudslay,  1889-1902:  I,  pi.  109,  glyphs  CI  Dl,  A2. 


230 


BUREAU  OF  AMEEICAN  ETHNOLOGY 


[bull.  57 


therefore  indicates  the  epoch  or  position  of  Zoomorph  G  in  the  Long 
Count,  because  it  alone  appears  as  an  Initial  Series.  In  the  case  of  all 
the  other  monuments  at  Quirigua/  where  there  is  but  one  Initial 
Series  in  the  inscription,  that  Initial  Series  marks  the  position 
of  the  monument  in  the  Long  Count.  It  seems  likely,  therefore, 
judging  from  the  general  practice  at  Quirigua,  that  9. 17. 15. 0.0  5  Ahau 
3  Muan  was  the  contemporaneous  date  of  Zoomorph  G,  not  10.0.0.0.0 
7  Ahau  18  Zip,  that  is,  the  Initial  Series  corresponding  to  the  Period- 
ending  date  here  imder  discussion  (see  pi.  22,  F)} 

Other  features  of  this  text  point  to  the  same  conclusion.  In  addi- 
tion to  the  Initial  Series  on  this  monument  there  are  upward  of  a 
dozen  Secondary-series  dates,  all  of  which  except  one  lead  to 
9.17.15.0.0  5  Ahau  3  Muan.  Moreover,  this  latter  date  is  recorded 
thrice  in  the  text,  a  fact  which  points  to  the  conclusion  that  it  was 
the  contemporaneous  date  of  this  monument. 

There  is  still  another,  perhaps  the  strongest  reason  of  all,  for  believ- 
ing that  Zoomorph  G  dates  from  9.17.15.0.0  6  Aha  a  3  Muan  rather 
than  from  10.0.0.0.0  7  Ahau  18  Zip.  If  assigned  to  the  former  date, 
every  hotun  from  9.15.15.0.0  9  Ahau  18  Xul  to  9.19.0.0.0  9  Ahau  18 
Mol  has  its  corresponding  marker  or  period-stone  at  Quirigua,  there 
being  not  a  single  break  in  the  sequence  of  the  fourteen  monuments 
necessary  to  mark  the  thirteen  hotun  endings  between  these  two  dates. 
If,  on  the  other  hand,  the  date  10.0.0.0.0  7  Ahau  18  Zip  is  assigned  to 
this  m.onument,  the  hotun  ending  9.17.15.0.0  5  Ahau  3  Muan  is  left 
without  its  corresponding  monument  at  this  city,  as  are  also  all  the 
hotuns  after  9.19.0.0.0  9  Ahau  18  Mol  up  to  10.0.0.0.0  7  Ahau  18  Zip, 
a  total  of  four  in  all.  The  perfect  sequence  of  the  monuments  at 
Quirigua  developed  by  regarding  Zoomorph  G  as  dating  from 
9.17.15.0.0  5  Ahau  3  Muan>  and  the  very  fragmentary  sequence  which 
arises  if  it  is  regarded  as  dating  from  10.0.0.0.0  7  Ahau  18  Zip,  is  of 
itself  practically  sufficient  to  prove  that  the  former  is  the  correct  date, 
and  when  taken  into  consideration  with  the  other  points  above  men- 
tioned leaves  no  room  for  doubt. 

If  this  is  true,  as  the  writer  believes,  the  date  ''Cycle  10  ending  on 
7  Ahau  18  Zip"  on  Zoomorph  G  is  ''prophetic"  in  character,  since  it 
did  not  occur  until  nearly  45  years  after  the  erection  of  the  monu- 
ment upon  which  it  was  recorded,  at  which  time  the  city  of  Quirigua 
had  probably  been  abandoned,  or  at  least  had  lost  her  prestige. 

Another  Cycle-10  ending  date,  which  differs  from  the  preceding  in 
that  it  is  almost  surely  contemporaneous,  is  that  on  Stela  11  at  Seibal, 

1  This  excludes  Stela  C,  which  has  two  Initial  Series  (see  figs.  68  and  77),  though  neither  of  them,  as 
explained  on  p.  175,  footnote  1,  records  the  date  of  this  moniiment.  The  true  date  of  this  monument  is 
declared  by  the  Period-ending  date  figured  in  pi.  21,  H,  which  is  9.17.0.0.0  6  Ahau  13  Kayab.  (See  p. 
226.) 

2  See  Maudslay,  1889-1902:  ii,  pi.  44,  west  side,  glyphs  G4  H4,  F5. 


MORLEY]      INTKODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


281 


the  latest  of  the  great  southern  sites. ^  This  is  %urecl  in  phite  22,/>. 
Glyphs  1  and  2  show  very  clearly  the  date  7  Ahaii  18  Zip,  and  <2:lypli 
3  declares  this  to  be'^at  the  end  of  Cycle  10."  ^  Compare  tlie  (vndin^;- 
sign  superfix  in  glyph  3  with  figure  37,  a-h.  This  glyph  is  followed 
by  1  katun  in  4,  which  in  turn  is  followed  by  the  date  5  Ahau  3  Kayab 
in  5  and  6.  Finally,  glyph  7  declares  ''The  end  of  Katun  1."  Count- 
ing forward  1  katun  from  10.0.0.0.0  7  Aliau  18  Zip,  the  date  reached 
will  be  5  Ahau  3  Kayab,  as  recorded  by  5  and  6,  and  the  Initial  Sc^ries 
corresponding  to  this  date  will  be  10.1.0.0.0  5  Ahau  3  Kayab,  as 
declared  by  glyph  7.    See  below: 

10.0.0.0.0    7  Ahau  18  Zip 
1.0.0.0 

10.1.0.0.0    5  Ahau  3  Kayab 

End  of  Katun  1. 

This  latter  date  is  found  also  on  Stelae  8,  9,  and  10,  at  the  same 
city. 

Another  Cycle-10  ending  date  which  was  probably  "  prophetic",  like 
the  one  on  Zoomorph  G  at  Quirigua,  is  figured  on  Altar  S  at  Copan 
(see  fig.  81).  In  the  first  glyph  on  the  left  appears  an  Initial-series 
introducing  glyph;  this  is  followed  in  glyphs  1-3  by  the  Initial- 
series  number  9.15.0.0.0,  which  the  student  will  find  leads  to  the 
terminal  date  4  Ahau  13  Yax  recorded  in  glyph  4.  This  whole 
Initial  Series  reads,  therefore,  9.15.0.0.0  4  Ahau  13  Yax.  In  glyph 
6a  is  recorded  5  katuns  and  in  glyph  7  the  date  7  Ahau  18  Zip,  in 
other  words,  a  Secondary  Series.^  Reducing  the  number  in  glyph 
6a  to  units  of  the  first  order,  we  have: 

6a  =  5X7,  200  =  36,  000 
fox     360=  0 
Not  recorded  OX      20=  0 
[ox       1=  0 

36,000 

Counting  this  number  forward  from_  the  date  4  Ahau  13  Yax,  the 
terminal  date  reached  will  be  found  to  agree  with  the  date  recorded 
in  glyph  7,  7  Ahau  18  Zip.  But  turning  to  our  text  again,  we  find 
that  this  date  is  declared  by  glyph  8a  to  be  at  the  end  of  Cycle  10. 
Compare  the  ending  sign,  which  appears  as  the  superfix  in  glyph  8a, 
with  figure  37,  a~Ji.    Therefore  the  Secondary-series  date  7  Ahau  18 

1  The  dates  10.2.5.0.0  9  Ahau  18  Yax  and  10.2.10.0.0  2  Ahau  13  Chen  on  Stelsc  1  and  2,  respectively,  at 
Quen  Santo,  are  purposely  excluded  from  this  statement.  Qxien  Santo  is  in  the  highlands  of  GuatemaJa 
(see  pi.  1)  and  is  well  to  the  south  of  the  Usamaclntla  region.  It  rose  to  prominence  probably  after  the 
collapse  of  the  great  southern  cities  and  is  to  be  considered  as  inaugurating  a  new  order  of  things,  if  not 
indeed  a  new  civilization. 

2  See  Maler,  1908  a:  iv,  No.  1,  pi.  9,  glyphs  E2,  F2,  \3,  and  A4. 

3  The  student  wiUnote  that  the  lower  periods  (the  tun,  uinal,  and  km  signs)  are  omitted  and  consequently 
are  to  be  considered  as  having  the  coefficient  0. 


232 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


Zip,  there  recorded,  closed  Cycle  10.  The  same  fact  could  have  been 
determined  by  adding  the  Secondary-series  number  in  glyph  6  a  to 
the  Initial-series  number  of  the  starting  point  4  Ahau  13  Yax  in 
glyphs  1-3: 

9.15.0.0.0    4  Ahau  13  Yax 

5.(0.0.0) 
10.  0.0.0.0    7  Ahau  18  Zip 


Fig.  81.   The  Initial  Series,  Secondary  Series,  and  Period-ending  date  on  Altar  S,  Copan. 

The  "  end  of  Cycle  10  "  in  glyph  8a  is  merely  redundancy.  The  writer 
believes  that  9.15.0.0.0  4  Ahau  13  Yax  indicates  the  present  time  of 
Altar  S  rather  than  10.0.0.0.0  7  Ahau  18  Zip,  and  that  consequently 
the  latter  date  was  '^prophetic"  in  character,  as  was  the  same  date 
on  Zoomorph  G  at  Quirigua.    One  reason  which  renders  this  prob- 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57    PLATE  23 


INITIAL  SERIES,  SECONDARY  SERIES,  AND  PERIOD- 
ENDING  DATES  ON  STELA  3,   PIEDRAS  NEGRAS 


MOELBY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  233 

able  is  that  the  sculpture  on  Altar  S  very  closely  resembles  the 
sculpture  on  Stelae  A  and  B  at  Copan,  both  of  which  date  from 
9.15.0.0.0  4  Ahau  13  Yax.  A  possible  explanation  of  the  record  of 
Cycle  10  on  this  monument  is  the  following:  On  the  date  of  this 
monument,  9.15.0.0.0  4  Ahau  13  Yax,  just  three-fourths  of  Cycle  9 
had  elapsed.  This  important  fact  would  hardly  have  escaped  the 
attention  of  the  old  astronomer-priests,  and  they  may  have  used  this 
monument  to  point  out  that  only  a  quarter  cycle,  5  katuns,  was  left 
in  Cycle  9.  This  concludes  the  discussion  of  Cycle-10  Period-ending 
dates. 

The  student  will  note  in  the  preceding  example  (fig.  81)  that 
Initial-series,  Secondary-series,  and  Period-ending  dating  have  all 
been  used  together  in  the  same  text,  glyphs  1-4  recording  an  Initial- 
series  date,  glyphs  6a  and  7,  a  Secondary-series  date,  and  glyphs  7 
and  8a,  a  Period-ending  date.  This  practice  is  not  at  all  unusual  in 
the  inscriptions  and  several  texts  illustrating  it  are  figured  below. 

Texts  Recording  Initial  Series,  Secondary  Series,  and  Period 

Endings 

In  plate  23  is  shown  the  inscription  on  Stela  3  at  Piedras  Negras. 
The  introducing  glyph  appears  in  Al  and  is  followed  by  the  Initial- 
series  number  9.12.2.0.16  in  B1-B3.  This  number  reduced  to  units 
of  the  first  order  and  counted  forward  from  its  starting  point  will 
be  found  to  reach  the  terminal  date  5  Cib  14  Yaxkin,  which  the  student 
will  readily  recognize  in  A4-B7;  the  month-sign  indicator"  appear- 
ing very  ^clearly  in  A7,  with  the  coefficient  9  affixed  to  it.  Compare 
the  day  sign  in  A4  with  figure  16,  z,  and  the  month  sign  in  B7  with 
figure  19,  ^,  I.  The  Initial  Series  recorded  in  A1-A4,  B7  reads,  there- 
fore, 9.12.2.0.16  5  Cib  14  Yaxkin.  In  Cl  Dl  is  recorded  the  number 
0  kins,  10  uinals,  and  12  tuns;  that  is,  12.10.0,  the  first  of  several 
Secondary  Series  in  this  text.  Reducing  this  to  units  of  the  first 
order  and  counting  it  forward  from  the  terminal  date  of  the  Initial 
Series,  6  Cib  14  Yaxkin,  the  terminal  date  of  the  Secondary  Series 
will  be  found  to  be  1  Cib  14  Kankin,  which  the  student  will  find 
recorded  in  C2b  D2a.  The  Initial-series  value  of  this  latter  date 
may  be  calculated  as  follows : 

9.12   2.  0.16    5  Cib  14  Yaxkin 

12.10.  0 
9.12.14.10.16    1  Cib  14  Kankin 

Following  along  the  text,  the  next  Secondary-series  number  appears 
in  D4-C5aand  consists  of  10  kins,^  11  uinals,  1  tun,  and  1  katun;  that 


1  The  usual  positions  of  the  uinal  and  kin  coefficients  in  D4a  are  reversed,  the  kin  coefficient  10  standing 
ahovf  the  uinal  sign  instead  of  at  the  left  of  it.  The  calculations  show,  however,  that  10,  not  U,  is  the  kin 
coefficient. 


234 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


is,  1.1.11.10.  Reducing  this  number  to  units  of  the  first  order  and 
counting  it  forward  from  the  date  next  preceding  it  in  the  text,  that 
is,  1  Cib  14  Kankin  in  C2b  D2a,  the  new  terminal  date  reached  will 
be  4  Cimi  14  TJo,  which  the  student  will  find  recorded  in  D5-C6. 
Compare  the  day  sign  in  D5  with  figure  16,  li,  i,  and  the  month 
sign  in  C6  with  figure  19,  6,  c.  The  Initial-series  value  of  this  new 
date  may  be  calculated  from  the  known  Initial-series  value  of  the 
preceding  date : 

9.12.14.10.16    1  Cib  14  Kankin 

1.  1.11.10 
9.13.16.  4.  6    4  Cimi  14  Uo 

The  third  Secondary  Series  appears  in  El  and  consists  of  15  kins,^  8 
uinals,  and  3  tuns,  or  3.8.15.  Reducing  this  number  to  units  of  the 
first  order  and  counting  it  forward  from  the  date  next  preceding  it 
in  the  text,  4  Cimi  14  Uo,  in  D5-C6,  the  new  terminal  date  reached 
will  be  11  Imix  14  Yax,  which  the  student  will  find  recorded  in  E2  F2. 
The  day  sign  in  E2  appears,  as  is  very  unusual,  as  a  head  variant  of 
which  only  the  headdress  seems  to  show  the  essential  element  of  the 
day  sign  Imix.  Compare  E2  with  figure  16,  a,  6,  also  the  month 
sign  in  F2  with  figure  19,  C[,  r.  The  Initial  Series  of  this  new  terminal 
date  may  be  calculated  as  above : 

9.13.16.  4.  6      4  Cimi  14  Uo 
3.  8.15 

9.13.19.13.  1    11  Imix  14  Yax 

The  fourth  and  last  Secondary  Series  in  this  text  follows  in  F6  and 
consists  of  19  kins  and  4  uinals,  that  is,  4.19.  Reducing  this  number 
to  imits  of  the  first  order  and  counting  it  forward  from  the  date  next 
preceding  it  in  the  text,  11  Imix  14  Yax  in  E2  F2,  the  new  terminal 
date  reached  will  be  6  Aliau  13  Muan,  which  the  student  will  find 
recorded  in  F7-F8.  Compare  the  month  sign  in  F8  with  ^^yq  19, 
a'  y.  But  the  glyph  following  this  date  in  F9  is  very  clearly  an 
ending  sign;  note  the  hand,  tassel-like  postfix,  and  subfixial  element 
showing  the  curl  infix:,  all  of  which  are  characteristic  ending  elements 
(see  figs.  37,  l-q,  and  54).  Moreover,  in  FlO  is  recorded  ''the  end 
of  Katun  14."  Compare  the  ending  prefix  in  this  glyph  with  figure 
37,  a-h.  This  would  seem  to  indicate  that  the  date  in  F7-F8, 6  Ahau 
13  Muan,  closed  Katun  14  of  Cycle  9  of  the  Long  Count.  Whether 
this  be  true  or  not  may  be  tested  by  finding  the  Initial-series  value 
corresponding  to  6  Ahau  13  Muan,  as  above: 

9.13.19.13.  1    11  Imix  14  Yax 
4.19 

9.14.  0.  0.  0      6  Ahau  13  Muan 


1  In  this  number  also  the  positions  of  the  uinal  and  kin  coefficients  are  reversed. 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57    PLATE  24 


INITIAL  SERIES,  SECONDARY  SERIES,  AND  PERIOD-ENDING  DATES 
ON  STELA  E  (WEST  SIDE),  QUIRIGUA 


MOELEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


235 


This  shows  that  the  date  6  Ahau  13  Muan  closed  Katun  14,  as  glyphs 
F9-F10  declare.  This  may  also  be  verified  by  changing  "  the  end  of 
Katun  14"  recorded  in  F9-F10  into  its  corresponding  Initial-scries 
value,  9.14.0.0.0,  and  solving  for  the  terminal  date.  The  day  reached 
by  these  calculations  will  be  6  Ahau  13  Muan,  as  above.  This  text,  in 
so  far  as  it  has  been  deciphered,  therefore  reads: 


9.12.  2.  0.16 

5  Cib  14  Yaxkin 

A1-A4,  B7 

12.10.  0 

CI  Dl 

9.12.14.10.16 

1  Cib  14  Kankin 

C2b  D2a 

1.  1.11.10 

D4-C5a 

9.13.16.  4.  6 

4  Cimi  14  TJo 

D5-C6 

3.  8.15 

El 

9.13.19.13.  1 

11  Imix  14  Yax 

E2  F2 

4.19 

F6 

9.14.  0.  0.  0 

6  Ahau  13  Muan 

F7-F8 

End  of  Katun  14 

F9-F10 

The  inscription  just  deciphered  is  worthy  of  special  note  for  several 
reasons.  In  the  first  place,  all  its  dates  and  numbers  are  not  only 
exceedingly  clear,  thus  facilitating  their  identification,  but  also  unusu- 
ally regular,  the  numbers  being  counted  forward  from  the  dates  next 
preceding  them  to  reach  the  dates  next  following  them  in  every  case ; 
all  these  features  make  this  text  particularly  well  adapted  for  study 
by  the  beginner.  In  the  second  place,  this  inscription  shows  the 
three  principal  methods  employed  by  the  Maya  in  recording  dates, 
that  is,  Initial-series  dating,  Secondary-series  dating,  and  Period-end- 
ing dating,  all  combined  in  the  same  text,  the  example  of  each  one 
being,  moreover,  unusually  good.  Finally,  the  Initial  Series  of  this 
inscription  records  identically  the  same  date  as  Stela  1  at  Piedras 
Negras,  namely,  9.12.2.0.16  5  Cib  14  Yaxkin.  Compare  plate  23 
with  plate  17.  Indeed,  these  two  monuments,  Stelse  1  and  3,  stand 
in  front  of  the  same  building.  All  things  considered,  the  inscription 
on  Stela  3  at  Piedras  Negras  is  one  of  the  most  satisfactory  texts 
that  has  been  found  in  the  whole  Maya  territory. 

Another  example  showing  the  use  of  these  three  methods  of  dating 
in  one  and  the  same  text  is  the  inscription  on  Stela  E  at  Quirigua, 
illustrated  in  plate  24  and  figure  82}  This  text  begms  with  the  Initial 
Series  on  the  west  side.  The  introducing  glyph  appears  in  A1-B3 
and  is  followed  by  the  Initial-series  number  9.14.13^4.17  in  A4-A6. 
Reducing  this  munber  to  units  of  the  first  order,  remembering  the 
correction  in  the  tun  coefiicient  in  A5  noted  below,  and  applying  the 
rules  previously  given  for  solving  Initial  Series,  the  terminal  date 

1  For  the  full  text  of  this  inscription,  see  Maudslay,  1889-1902:  ii,  pis.  28-32. 

2  The  student  will  note  that  12,  not  13,  tuns  are  recorded  in  A5.  As  explained  elsewhere  (see  pp.  247, 248), 
this  is  an  error  on  the  part  of  the  ancient  scribe  who  engraved  this  inscription.  The  correct  tun  coefficient 
is  13,  as  used  above. 


236 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


reached  will  be  12  Gaban  5  Kayab.  This  the 
student  will  readily  recognize  in  B6-B8b. 
the  form  in  B8a  being  the  ''month  sign 
indicator/'  here  shown  with  a  head-variant 
coefficient  10.  Compare  B6  with  figure 
16,  a',  h',  and  B8b  with  figure  19,  d'-f. 
This  Initial  Series  therefore  should  read 
as  follows:  9.14.13.4.17  12  Caban  5  Kayab. 
Following  down  the  text,  there  is  reached 
in  BlOb-Alla,  a  Secondar3^-series  number 
consisting  of  3  kins,  13  uinals,  and  6  tuns, 
that  is,  6.13.3.  Counting  this  number  for- 
ward from  the  date  next  preceding  it  in 
the  text,  12  Caban  5  Kayab,  the  date 
reached  will  be  4  Abau  13  Yax,  which  the 
student  will  find  recorded  in  Bll.  Com- 
pare the  month  form  in  Bllb  with  figure 
19,  r.  But  since  the  Initial-series  value 
of  12  Caban  6  Kayab  is  known,  the  Initial- 
series  value  of  4  Ahau  13  Yax  may  be  cal- 
culated from  it  as  follows: 


9.14.13.  4.17 
6.13.  3 
9.15.  0.  0.  0 


12  Caban  5  Kayab 


4  Abau  13  Yax 


C 


The  next  Secondary-series  number  ap- 
pears in  Bl2,  plate  24,  B,  and  consists  of 
6  kins,  14  uinals,  and  1  tun,  that  is,  1.14.6.^ 
The  student  "will  find  that  all  efforts  to 
reach  the  next  date  recorded  in  the  text, 
6  Cimi  4  Tzec  in  Al3b  Bl3a,  by  counting 
forward  1.14.6  from  4  Ahau  13  Yaxin  Bll, 
the  date  next  preceding  this  number,  will 
prove  unsuccessful.  However,  by  count- 
ing hackward  1.14.6  from  6  Cimi  4  Tzec,  he 
ryx  will  find  the  date  from  which  the  coimt 
J_  proceeds  is  10  Ahau  8  Chen,  though  this 
latter  date  is  nowhere  recorded  in  this  text. 
We  have  seen  elsewhere,  on  Stela  F  for  ex- 
ample (pi.  19,  A,  B),  that  the  date  6  Cimi 
4  Tzec  corresponded  to  the  Initial-series 
number  9.15.6.14.6;  consequently,  we  may 
calculate  the  position  of  the  unrecorded 

FIG.  82.  The  Initial  Series  on  Stela  E  "TThis  Seconda^^^ei^Tniiinb^  is  doubly  irregular.  In  the 
(east  side),  Quingua.  ^^^^  p^^^^^  ^.^^^  coefficients  are  reversed,  the  latter 

standing  to  the  left  of  its  sign  instead  of  above,  and  in  the  second  place,  the  uinal  coefficient,  although  it  is 
14,  has  an  ornamental  dot  between  the  two  middle  dots. 


MOELEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


237 


date  10  Ahau  8  Chen  in  the  Long  Count  from  this  known  Initial 
Series,  by  subtracting  ^  L14.6  from  it: 

9.15.6.14.6     6  Cimi  4  Tzec 
1.14.6 

9.15.5.  0.0    10  Ahau  8  Chen 

We  now  see  that  there  are  5  tuns,  that  is,  1  hotun,  not  recorded  here, 
namely,  the  hotun  from  9.15.0.0.0  4  Ahau  13  Yax,  to  9.15.5.0.0  10 
Ahau  8  Chen,  and  further,  that  the  Secondary-series  number  1.14.6 
in  B12  is  counted  from  the  unexpressed  date  10  Ahau  8  Chen  to  reach 
the  terminal  date  6  Cimi  4  Tzec  recorded  in  Al3b  Bl3a. 

The  next  Secondary-series  number  appears  in  Al4b  Bl4  and 
consists  of  15  kins,  16  uinals,  1  tun,  and  1  katun,  that  is,  1.1.16.15. 
As  in  the  preceding  case,  however,  all  efforts  to  reach  the  date  fol- 
lowing this  number,  11  Imix  19  Muan  in  Al5b  Bl5a,  by  counting  it 
forward  from  6  Cimi  4  Tzec,  the  date  next  preceding  it  in  the  text, 
will  prove  unavailing.  As  before,  it  is  necessary  to  count  it  laclc- 
ward  from  11  Imix  19  Muan  to  determine  the  starting  point.  Per- 
forming this  operation,  the  starting  point  will  be  found  to  be  tJie 
date  7  Cimi  9  Zotz.  Since  neither  of  these  two  dates,  11  Imix  19 
Muan  and  7  Cimi  9  Zotz,  occurs  elsewhere  at  Quirigua,  we  must  leave 
their  corresponding  Initial-series  values  indeterminate  for  the  present. 

The  last  Secondary  Series  in  this  text  is  recorded  in  Al7b  Bl7a 
and  consists  of  19  khis,^  4  uinals,  and  8  tuns.  Reducing  this  number 
to  units  of  the  first  order  and  counting  it  forward  from  tne  date  next 
preceding  it  in  the  text,  11  Imix  19  Muan  in  Al5b  Bl5a,  the  terminal 
date  reached  will  be  13  Ahau  18  Cumhu,  which  the  student  will  find 
recorded  in  A18.  Compare  the  month  sign  with  figure  19,  f/\  V . 
But  immediately  following  this  date  in  B  18a  is  Katun  17  and  in  the 
upper  part  of  Bl8b  the  hand-denoting  ending.  These  glyphs  Al8 
and  B18  would  seem  to  indicate,  therefore,  that  Katun  17  came  to 
an  end  on  the  date  13  Ahau  18  Cumhu.  That  they  do,  may  be  proved 
beyond  all  doubt  by  changing  this  period  ending  into  its  corresponding 
Initial-series  number  9.17.0.0.0  and  solving  for  the  terminal  date. 
This  will  be  found  to  be  13  Ahau  18  Cumhu,  which  is  recorchnl  in 
A18.  This  latter  date,  therefore,  had  the  fpllowmg  position  in  the 
Long  Count:  9.17.0.0.0  13  Ahau  18  Cumhu.  But  having  determined 
the  position  of  this  latter  date  in  the  Long  Count,  that  is,  its  Initial- 
series  value,  it  is  now  possible  to  fix  the  positions  of  the  two  dntes 
11  Imix  19  Muan  and  7  Cimi  9  Zotz,  which  we  were  obliged  to  leave 
indeterminate  above.    Since  the  date  13  Ahau  18  Cumhu  was  derived 

'  Since  we  counted  backward  1.14.6  from  6  Cimi  4  Tzec  to  reach  10  Ahau  8  Chen,  we  must  nvMracl  1.14.6 
from  the  Initial-series  value  of  6  Cimi  4  Tzec  to  reach  the  Initial-series  value  of  10  Ahau  8  Chen. 

2  It  is  obvious  that  the  kin  and  uinal  coefficients  are  reversed  in  A  17b  since  the  coefficient  above  the  umal 
sign  is  very  clearly  19,  an  impossible  value  for  the  uinal  coefficient  in  the  inscriptions,  19  uinals  always 
being  written  1  tun,  1  uinal.  Therefore  the  19  must  be  the  kin  coefficient.  See  also  p.  110,  footnote  1. 


238 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


by  counting  forward  8.4.19  from  11  Imix  19  Muan,  the  Initial-series 
value  of  the  latter  maybe  calculated  by  subtracting  8.4.19  from  the 
Initial -series  value  of  the  former: 


And  since  the  date  11  Imix  19  Muan  was  reached  by  counting  for- 
ward 1.1.16.15  from  7  Cimi  9  Zotz,  the  Initial-series  value  of  the  latter 
may  be  calculated  by  subtracting  1.1.16.15  from  the  now  known 
Initial-series  value  of  the  former: 


Although  this  latter  date  is  not  recorded  in  the  text,  the  date  next 
preceding  the  number  1.1.16.15  is  6  Cimi  4  Tzee,  which  corresponded 
to  the  Initial  Series  9.15.6.14.6  6  Cimi  4  Tzee,  as  we  have  seen,  a 
date  which  was  exactly  3  tuns  earlier  than  7  Cimi  9  Zotz,  9.15.9.14.6- 
9.15.6.14.6  =  3.0.0. 

The  inscription  on  the  west  side  closes  then  in  Al8  B18  with  the 
record  that  Katun  17  ended  on  the  date  13  Ahau  18  Cumhu.  The 
inscription  on  the  east  side  of  this  same  monument  opens  with  this 
same  date  expressed  as  an  Initial  Series,  9.17.0.0.0  13  Ahau  18  Cumhu. 
See  figure  82,  A1-A6,  A7,i  and  AlO. 

The  reiteration  of  this  date  as  an  Initial  Series,  when  its  position 
in  the  Long  Count  had  been  fixed  unmistakably  on  the  other  side  of 
the  same  monument  by  its  record  as  a  Period-ending  date,  together 
with  the  fact  that  it  is  the  latest  date  recorded  in  this  inscription, 
very  clearly  indicates  that  it  alone  designated  the  contemporaneous 
time  of  Stela  E,  and  hence  determines  the  fact  that  Stela  E  was  a 
hotun-marker.  This  whole  text,  in  so  far  as  deciphered,  reads  as 
follows : 

West  side:  9.14.13.^4.17    12  Caban  5  Kayab    Plate 24, ^Al-B6,B8b 


9.17.  0.  0.  0    13  Ahau  18  Cumhu 
8.  4.19 

9.16.11.13.  1    11  Imix  19  Muan 


9.16.11.13.  1    11  Imix  19  Muan 

1.  1.16.15 
9.15.  9.14.  6     7  Cimi  9  Zotz 


6.13.  3  . 

9.15.  0.  0.  0      4  Ahau  13  Yax 

[5.  0.  0] 
9.15.  5.  0.  0    10  Ahau  8  Chen 

1.14.  6 

9.15.  6.14.  6      6  Cimi  4  Tzee 
[3.  0.  0] 


Plate  24,  ^,B10b-Alla 
Plate  24,  A,  Bll 
Undeclared 


Plate  24,  B,  B12 
Plate  24,  B.  Al3b  B13a 
Undeclared 


1  The  first  glyph  of  the  Supplementary  Series,  B6a,  very  irregularly  stands  between  the  kin  period  glyph 
and  the  day  part  of  the  terminal  date. 

2  Incorrectly  recorded  as  12.   See  pp.  247,  248. 


MORLET]      INTEODUCTION  TO  STUDY  OP  MAYA  HIEROGLYPHS  239 


9.15.  9.14.  6 

1.  1.16.15 
9.16.11.13.  1 
8.  4.19 
9.17.  0.  0.  0 

End  of  Katun  17 
East  side:  9.17.  0.  0.  0 


7  Cimi  9  Zotz 


11  Imix  19  Muan 


13  Ahau  18  Cumhu 


13  Ahau  18  Cumhu 


Undeclared 
Plate  24,  jB,Al4l)Bl4 
Plate  24,5,  Al5b  Bl5a. 
Plate  24,  B,  Al7b  B17a 
Plate  24,  B,  Al8 
Plate  24,  B,  B18 
Figure  82,  A1-A6,  A7, 
AlO 


Comparing  the  summary  of  the  inscription  on  Stela  E  at  Quirigua, 
just  given,  with  the  summaries  of  the  inscriptions  on  Stelae  J  and  F, 
and  Zoomorph  G,  at  the  same  city,  all  four  of  which  are  shown  side 
by  side  in  Table  XVII, ^  the  interrelationship  of  these  four  monu- 
ments appears  very  clearly. 

Table  XVII.  INTERRELATIONSHIP  OF  DATES  ON  STEL^  E,  F.  AND  J 
AND  ZOOMORPH  G,  QUIRIGUA 


Date 

Stela  J 

stela  F 

stela  E 

Zoomorph 
G 

9.14.13.  4.17 

12  Caban  6  Kayab 

X 

X 

X 

X 

9.15.  0.  0. 

0 

4  Ahau  13  Yax 

X 

X 

9.15.  5.  0. 

0 

10  Ahau  8  Chen 

X 

X 

9.15.  6.14. 

6 

6  Cimi  4  Tzec 

X 

X 

X 

X 

9.15.  9.14. 

6 

7  Cimi  9  Zotz 

X 

9.15.10.  0. 

0 

3  Ahau  3  Mol 

X 

9.16.  5.  0. 

0 

8  AHAU  8  ZOTZ 

X 

9.16.10.  0. 

0 

1  AHAU  3  ZIP 

X 

9.16.11.13. 

1 

11  Imix  19  Muan 

X 

9.17.  0.  0. 

0 

13  AHAU  18  CUMHU 

X 

9.17.15.  0. 

0 

5  AHAU  3  MUAN 

X 

In  spite  of  the  fact  that  each  one  of  these  four  monuments  marks  a 
different  hotun  in  the  Long  Count,  and  consequently  dates  from  a 
different  period,  all  of  them  go  back  to  the  same  date,  9.14.13.4.17 
12  Caban  5  Kayab,  as  their  original  starting  point  (see  above).  This 
date  would  almost  certainly  seem,  therefore,  to  indicate  some  very 
important  event  in  the  annals  of  Quirigua.  Moreover,  since  it  is 
the  earhest  date  found  at  this  city  which  can  reasonably  be  regarded 
as  having  occurred  during  the  actual  occupancy  of  the  site,  it  is  not 
unprobable  that  it  may  represent,  as  explained  elsewhere,  the  time 
at  which  Quirigua  was  founded. ^    It  is  necessary,  however,  to  cau- 

1  In  this  table  the  numbers  showing  the  distances  have  been  omitted  and  all  dates  are  sho\vB  in  terms 
of  their  corresponding  Initial-series  numbers,  in  order  to  facilitate  their  comparison.  The  contempo- 
raneous date  of  each  monument  is  given  in  bold-faced  figures  and  capital  letters,  and  the  student  will 
note  also  that  this  date  not  only  ends  a  hotun  in  each  case  but  is,  further,  the  latest  date  in  each  text. 

2  The  Initial  Series  on  the  west  side  of  Stela  D  at  Quirigua  is  9.16.13.4.17  8  Caban  5  Yaxkin,  which  was 
just  2  katuns  later  than  9.14.1.3.4.17  12  Caban  5  Kayab,  or,  in  other  words,  the  second  katun  anniversary, 
if  the  term  anniversary  may  be  thus  used,  of  the  latter  date. 


240 


BUREAU  OF  AMEEICAN  ETHNOLOGY 


[BULL.  57 


tion  the  student  that  the  above  explanation  of  the  date  9.14.13.4.17 
12  Caban  5  Kayab,  or  indeed  any  other  for  that  matter,  is  in  the 
present  state  of  our  knowledge  entirely  a  matter  of  conjecture. 

Passing  on,  it  will  be  seen  from  Table  XVII  that  two  of  the  monu- 
ments, namely.  Stelae  E  and  F,  bear  the  date  9.15.0.0.0  4  Ahau  3 
Yax,  and  two  others,  Stelse  E  and  J,  the  date  9.15.5.0.0  10  Ahau  8 
Chen,  one  hotun  later.  All  four  come  together  again,  however, 
with  the  date  9.15.6.14.6  6  Cimi  4  Tzec,  which  is  recorded  on  each. 
This  date,  like  9.14.13.4.17  12  Caban  5  Kayab,  designates  probably 
another  important  event  in  Quirigua  history,  the  nature  of  which, 
however,  again  escapes  us.  After  the  date  9.15.6.14.6  6  Cimi  4  Tzec, 
these  monuments  show  no  further  correspondences,  and  we  may  pass 
over  the  intervening  time  to  their  respective  closing  dates  with  but 
scant  notice,  with  the  exception  of  Zoomorph  G,  which  records  a 
half  dozen  dates  in  the  hotun  that  it  marks,  9.17.15.0.0  5  Ahau  3 
Muan.    (These  latter  are  omitted  from  Table  XVII.) 

This  concludes  the  presentation  of  Initial-series,  Secondary -series, 
and  Period-ending,  dating,  with  which  the  student  should  be  suffi- 
ciently familiar  by  this  time  to  continue  his  researches  independently. 

It  was  explained  (see  p.  76)  that,  when  a  Secondary-series  date 
could  not  be  referred  ultimately  to  either  an  Initial-series  date 
or  a  Period-ending  date,  its  position  in  the  Long  Count  could 
not  be  determined  with  certainty,  and  furthermore  that  such  a  date 
became  merely  one  of  the  18,980  dates  of  the  Calendar  Round  and 
could  be  fixed  only  within  a  period  of  52  years.  A  few  examples  of 
Calendar-round  dating  are  given  in  figure  83  and  plate  25.  In 
figure  83,  A,  is  shown  a  part  of  the  inscription  on  Altar  M  at  Quirigua.* 
In  Al  Bl  appears  a  number  consisting  of  0  kins,  2  uinals,  and  3  tuns, 
that  is,  3.2.0,  and  following  this  in  A2b  B2,  the  date  4  Ahau  13  Yax, 
and  in  A3b  B3  the  date  6  Ahau  18  Zac.  Compare  the  month  glyphs 
in  B2  and  B3  with  q  and  r,  and  s  and  t,  respectively,  of  figure  19. 
This  has  every,  appearance  of  being  a  Secondary  Series,  one  of  the 
two  dates  being  the  starting  point  of  the  number  3.2.0,  and  the 
other  its  terminal  date.  Reducing  3.2.0  to  units  of  the  first  order, 
we  have: 

Bl  =3X360  =  1,080 
A1=2X  20=  40 
A1=0X     1=  0 

1,120 

Counting  this  number  forward  from  4  Ahau  13  Yax,  the  nearest  date 
to  it  in  the  text,  the  terminal  date  reached  will  be  found  to  be  6  Ahau 
18  Zac,  the  date  which,  we  have  seen,  was  recorded  in  A3b  B3.  It 


1  For  the  full  text  of  this  inscription,  see  Maudslay,  1889-1902:  n,  pi.  50. 


CALENDAR-ROUND   DATES  ON  ALTAR 


5,  TIKAL 


MOELEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEKO(i  L  V IM  I  S 


241 


is  clear,  therefore,  that  this  text  records  the  fact  that  3.2.0  has  been 
counted  forward  from  the  date  4  Ahau  13  Yax  and  the  date  6  Ahau 
18  Zac  has  been  reached,  but  there  is  notlung  given  by  means  of 
which  the  position  of  either  of  these  dates  in  the  Long  Count  can  be 
determined;  consequently  either  of  these  dates  will  be  found  recur- 
ring like  any  other  Calendar-round  date,  at  intervals  of  every  52 
years.  In  such  cases  the  first  assumption  to  be  made  is  that  one  of 
the  dates  recorded  the  close  of  a  hotun,  or  at  least  of  a  tun,  in  Cycle 
9  of  the  Long  Count.    The  reasons  for  this  assumption  are  quite  ob- 


A  B 

Fig.  83.    Calendar-round  dates:  A,  Altar  M,  Quirigua;  B,  Altar  Z,  Copan. 


vious.  The  overwhelming  majority  of  Maya  dates  fall  in  Cycle  9,  and 
nearly  all  inscriptions  have  at  least  one  date  which  closed  some  hotun 
or  tun  of  that  cycle.  Referring  to  Goodman's  Tables,  in  which  the 
tun  endings  of  Cycle  9  are  given,  the  student  will  find  that  the  date 
4  Ahau  13  Yax  occurred  as  a  tun  ending  in  Cycle  9,  at  9.15.0.0.0 
4  Ahau  13  Yax,  in  which  position  it  closed  not  only  a  hotun  but  also 
a  katun.  Hence,  it  is  probable,  although  the  fact  is  not  actually 
recorded,  that  the  Initial-series  value  of  the  date  4  Ahau  13  Yax  m 
this  text  is  9.15.0.0.0  4  Ahau  13  Yax,  and  if  this  is  so  the  Initial-series 
value  of  the  date  6  Ahau  18  Zac  will  be: 

9.15.0.0.0    4  Ahau  13  Yax 
3.2.0 

9.15.3.2.0    6  Ahau  18  Zac 
43508°— Bull.  57—15  16 


242 


BUREAU  OF  AMERICAN  ETHNOLOGY 


I  BULL.  57 


In  the  case  of  this  particular  text  the  Initial-series  value  9.15.0.0.0 
might  have  been  assigned  to  the  date  4  Ahau  13  Yax  on  the  ground 
that  this  Initial-series  value  appears  on  two  other  monuments  at 
Quirigua,  namely,  Stelae  E  and  F,  with  this  same  date. 

In  figure  83,  is  shown  a  part  of  the  inscription  from  Altar  Z  at 
Copan.^  In  Al  Bl  appears  a  number  consisting  of  1  kin,  8  uinals, 
and  1  tun,  that  is,  1.8.1,  and  following  this  in  B2-A3  is  the  date  13 
Ahau  18  Cumhu,  but  no  record  of  its  position  in  the  Long  Count. 
If  13  Ahau  18  Cumhu  is  the  terminal  date  of  the  number  1.8.1,  the 
starting  point  can  be  calculated  by  counting  this  number  backward, 
giving  the  date  12  Cauac  2  Zac.  On  the  other  hand,  if  13  Ahau  18 
Cumhu  is  the  starting  point,  the  terminal  date  reached  by  counting 
1.8.1  forward  will  be  1  Imix  9  Mol.  However,  since  an  ending  prefix 
appears  just  before  the  date  13  Ahau  18  Cumhu  in  A2  (compare  fig. 
37,  a-h) ,  and  since  another,  though  it  must  be  admitted  a  very  unusual 
ending  sign,  appears  just  after  this  date  in  A3  (compare  the  prefix 
of  B3  with  the  prefix  of  fig.  37,  o,  and  the  subfix  with  the  subfixes 
of  l-n  and  g  of  the  same  figure),  it  seems  probable  that  13  Ahau  18 
Cumhu  is  the  terminal  date  and  also  a  Period-ending  date.  Referring 
to  Goodman's  Tables,  it  will  be  found  that  the  only  tun  in  Cycle  9 
which  ended  with  the  date  13  Ahau  18  Cumhu  was  9.17.0.0.0  13  Ahau 
18  Cumhu,  which  not  only  ended  a  hotun  but  a  katun  as  well.^  If 
this  is  true,  the  unrecorded  starting  point  12  Cauac  2  Zac  can  be 
shown  to  have  the  following  Initial-series  value: 

9.17.  0.0.  0    13  Ahau  18  Cumhu 

1.8.  1  Backward 
9.16.18.9.19    12  Cauac  2  Zac 

In  each  of  the  above  examples,  as  we  have  seen,  there  was  a  date 
which  ended  one  of  the  katuns  of  Cycle  9,  although  this  fact  was  not 
recorded  in  connection  with  either.  Because  of  this  fact,  however, 
we  were  able  to  date  both  of  these  monuments  with  a  degree  of  prob- 
ability amounting  almost  to  certainty.  In  some  texts  the  student 
will  find  that  the  dates  recorded  did  not  end  any  katun,  hotun,  or 
even  tun,  in  Cycle  9,  or  in  any  other  cycle,  and  consequently  such 
dates  can  not  be  assigned  to  their  proper  positions  in  the  Long  Count 
by  the  above  method. 

The  inscription  from  Altar  5  at  Tikal  figured  in  plate  25  is  a  case 
in  point.  This  text  opens  with  the  date  1  Muluc  2  Muan  in  glyphs 
1  and  2  (the  first  glyph  or  starting  point  is  indicated  by  the  star). 

1  For  the  full  text  of  this  inscription,  see  Maudslay,  1889-1902:  i,  pi.  112. 

2  Every  f.ourth  hotun  ending  in  the  Long  Count  was  a  katun  ending  at  the  same  time,  namely: 

9.16.  0.0.0  2  Ahau  13  Tzec 

9.16.  5.0.0  8  Ahau  8  Zotz 
9.16.10.0.0  lAhau  3  Zip 
9.16.15.0.0  7  Ahau  18  Pop 

9.17.  0.0.0  13  Ahau  18  Cumhu 
etc. 


MOELEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  243 


Compare  glyph  1  with  figure  16,  m,  n,  and  glyph  2  with  hgure  19, 
a',  V .  In  glyphs  8  and  9  appears  a  Secondary-series  number  con- 
sisting of  18  kins,  11  uinals,  and  11  tuns  (11.11.18).  Redjucing  this 
number  to  units  of  the  first  order  and  counting  it  forward  from  the 
date  next  preceding  it  in  the  text,  1  Muluc  2  Muan  in  glyphs  1  and  2, 
the  terminal  date  reached  will  be  13  Manik  0  Xul,  which  tlu^  stuck^it 
will  find  recorded  in  glyphs  10  and  11.  Compare  glyph  10  with 
figure  16,  j,  and  glyph  11  with  figure  19,  i,  j.  The  next  Secondary- 
series  number  appears  in  glyphs  22  and  23,  and  consists  of  19  kins, 
9  uinals,  and  8  tuns  (8.9.19) .  Reducing  this  to  units  of  the  first  order 
and  counting  forward  from  the  date  next  preceding  it  in  the  text,  13 
Manik  0  Xul  in  glyphs  10  and  11,  the  terminal  date  reached  will  be 
11  Cimi  19  Mac,  which  the  student  will  find  recorded  in  glyphs  24 
and  25.  Compare  glyph  24  with  figure  16,  h,  i,  and  glyph  25  with 
figure  19,  w,  x.  Although  no  number  appears  in  glyph  26,  there 
follows  in  glyphs  27  and  28  the  date  1  Muiuc  2  Kankin,  which  the 
student  will  find  is  just  three  days  later  than  11  Cimi  19  Mac,  that 
is,  one  day  12  Manik  0  Kankin,  two  days  13  Lamat  1  Kankin,  and 
three  days  1  Muluc  2  Kankin. 

In  spite  of  the  fact  that  all  these  numbers  are  counted  regularly 
from  the  dates  next  preceding  them  to  reach  the  dates  next  following 
them,  there  is  apparently  no  glyph  in  this  text  which  will  fix  the 
position  of  any  one  of  the  above  dates  in  the  Long  Count.  Moreover, 
since  none  of  the  day  parts  show  the  day  sign  Ahau,  it  is  evident 
that  none  of  these  dates  can  end  any  uinal,  tun,  katun,  or  cycle  in 
the  Long  Count,  hence  their  positions  can  not  be  determined  by  the 
method  used  in  fixing  the  dates  in  figure  83,  A  and  B. 

There  is,  however,  another  method  by  means  of  whicii  Calendar- 
round  dates  may  sometimes  be  referred  to  their  proper  positions  in 
the  Long  Count.  A  monument  which  shows  only  Calendar-round 
dates  may  be  associated  with  another  monument  or  a  building,  the 
dates  of  which  are  fixed  in  the  Long  Count.  In  such  cases  the  fixed 
dates  usually  will  show  the  positions  to  which  the  Calendar-round 
dates  are  to  be  referred. 

Taking  any  one  of  the  dates  given  on  Altar  5  in  plate  25,  as  the  last, 
1  Muluc  2  Kankin,  for  example,  the  positions  at  which  this  date 
occurred  in  Cycle  9  may  be  determined  from  Goodman's  Tables  to 
be  as  follows : 


9.  0.16.  5.9 
9.  3.  9.  0.9 
9.  6.  1.13.9 
9.  8.14.  8.9 
9.11.  7.  3.9 
9.13.19.16.9 
9.16.12.11.9 
9.19.  5.  6.9 


1  Muluc  2  Kankin 
1  Muluc  2  Kankin 
1  Muluc  2  Kankin 
1  Muluc  2  Kankin 
1  Muluc  2  Kankin 
1  Muluc  2  Kankin 
1  Muluc  2  Kankin 
1  Muluc  2  Kankin 


244 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


Next  let  us  ascertain  whether  or  not  Altar  5  was  associated  with  any 
other  monument  or  building  at  Tikal,  the  date  of  which  is  fixed 
unmistakably  in  the  Long  Count.  Says  Mr.  Teobert  Maler,  the  dis- 
coverer of  this  monument:^  ^^A  little  to  the  north,  fronting  the  north 
side  of  this  second  temple  and  very  near  it,  is  a  masonry  quadrangle 
once,  no  doubt,  containing  small  chambers  and  having  an  entrance 
to  the  south.  In  the  middle  of  this  quadrangle  stands  Stela  16  in 
all  its  glory,  still  unharmed,  and  in  front  of  it,  dee/ply  huried  in  the 
earth,  we  found  Circular  Altar  5,  which  was  destined  to  become  so 
widely  renowned."  It  is  evident  from  the  foregoing  that  the  altar 
we  are  considering  here,  caUed  by  Mr.  Maler  '^Circular  Altar  5,"  was 
found  in  connection  with  another  monument  at  Tikal,  namely, 
Stela  16.  But  the  date  on  this  latter  monument  has  already  been 
deciphered  as  '^6  Ahau  13  Muan  ending  Katun  14"  (see  pi.  21,  D; 
also  p.  224),  and  this  date,  as  we  have  seen,  corresponded  to  the 
Initial  Series  9.14.0.0.0  6  Ahau  13  Muan. 

Our  next  step  is  to  ascertain  whether  or  not  any  of  the  Initial- 
series  values  determined  above  as  belonging  to  the  date  1  Muluc  2 
Kankin  on  Altar  5  are  near  the  Initial  Series  9.14.0.0.0  6  Ahau  13 
Muan,  which  is  the  Initial-series  date  corresponding  to  the  Period- 
ending  date  on  Stela  16.  By  comparing  9.14.0.0.0  with  the  Initial- 
series  values  of  1  Muluc  2  Kankin  given  above  the  student  will  find 
that  the  fifth  value,  9.13.19.16.9,  corresponds  with  a  date  1  Muluc  2 
Kankin,  which  was  only  31  days  (1  uinal  and  11  kins)  earlier  than 
9.14.0.0.0  6  Ahau  13  Muan.  Consequently  it  may  be  concluded  that 
9.13.19.16.9  was  the  particular  day  1  Muluc  2  Kankin  which  the 
ancient  scribes  had  in  mind  when  they  engraved  this  text.  From 
this  known  Initial-series  value  the  Initial-series  values  of  the  other 
dates  on  Altar  5  may  be  obtained  by  calculation.  The  texts  on  Altar 
5  and  Stela  16  are  given  below  to  show  their  close  connection: 

Altar  5 


9.12.19.12.  9  1  Muluc  2  Muan      glyphs  1  and  2 

11.11.18  glyphs  8  and  9 

9.13.11.  6.  7  13  Manik  0  Xul       glyphs  10  and  11 

8.  9.19  glypl^s  22  and  23 

9.13.19.16.  6  11  Cimi  19  Mac       glyphs  24  and  25 

(3)  undeclared 

9.13.19.16.  9  1  Muluc  2  Kankin    glyphs  27  and  28 

(1.11)  (Time  between  the  two  monuments,  31  days.) 

Stela  16 

9.14.0.0.0  6  Ahau  13  Muan  A1-A4 


1  Maler,  1911:  No.  1,  p.  40. 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  IIIEROGLYPirS  245 


Sometimes,  however,  monuments  showing  Calenclar-rt)ujul  dates  stand 
alone,  and  in  such  cases  it  is  almost  impossible  to  fix  their  dates  in  the 
Long  Count.  At  Yaxchilan  in  particular  Calendar-round  dating 
seems  to  have  been  extensively  employed,  and  for  this  reason  less 
progress  has  been  made  there  than  elsewhere  in  deciphering  the 
inscriptions. 

Errors  in  the  Originals 

Before  closing  the  presentation  of  the  subject  of  the  Maya  inscrip- 
tions the  writer  has  thought  it  best  to  insert  a  few  texts  which  show 


C 

Fig.  84.    Texts  showing  actual  errors  in  the  originals:  A,  Lintel,  Yaxchilan;  B,  Altar  Q,  Copan;  C, 

Stela  23,  Naranjo. 

actual  errors  in  the  originals,  mistakes  due  to  the  carelessness  or  over- 
sight of  the  ancient  scribes. 

Errors  in  the  original  texts  may  be  divided  into  two  general  classes : 
(1)  Those  which  are  revealed  by  inspection,  and  (2)  those  which  do 
not  appear  until  after  the  indicated  calculations  have  been  made 
and  the  results  fail  to  agree  with  the  glyphs  recorded. 

An  example  of  the  first  class  is  illustrated  in  figure  84,  A.  A  very 
cursory  inspection  of  this  text — an  Initial  Series  from  a  lintel  at  Yax- 
chilan— will  show  that  the  uinal  coefficient  in  Cl  represents  an  impos- 
sible condition  from  the  Maya  point  of  view.    This  glyph  as  it  stands 


246 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


unmistakably  records  19  uinals,  a  number  which  had  no  existence  in 
the  Maya  system  of  numeration,  since  19  uinals  are  always  recorded 
as  1  tun  and  1  uinal.^  Therefore  the  coefficient  in  Cl  is  incorrect  on 
its  face,  a  fact  we  have  been  able  to  determine  before  proceeding  with 
the  calculation  indicated.  If  not  19,  what  then  was  the  coefficient 
the  ancient  scribe  should  have  engraved  in  its  place?  Fortunately 
the  rest  of  this  text  is  unusually  clear,  the  Initial-series  number 
9.15.6..?.!  appearing  in  Bl-Dl,  and  the  terminal  date  which  it 
reaches,  7  Imix  19  Zip,  appearing  in  C2  D2.  Compare  C2  with  figure 
16,  a,  h,  and  D2  with  figure  19,  d.  We  know  to  begin  with  that  the 
uinal  coefficient  must  be  one  of  tlie  eighteen  numerals  0  to  17,  inclu- 
sive. Trying  0  first,  the  number  will  be  9.15.6.0.1,  which  the  student 
will  find  leads  to  the  date  7  Imix  4  Chen.  Our  first  trial,  therefore, 
has  proved  unsuccessful,  since  the  date  recorded  is  7  Imix  19  Zip. 
The  day  parts  agree,  but  the  month  parts  are  not  the  same.  This 
month  part  4  Chen  is  useful,  however,  for  one  thing,  it  shows  us  how 
far  distant  we  are  from  the  month  part  19  Zip,  which  is  recorded. 
It  appears  from  Table  XV  that  in  counting  forward  from  position 
4  Chen  just  260  days  are  required  to  reach  position  19  Zip.  Conse- 
quently, our  first  trial  number  9.15.6.0.1  falls  short  of  the  number  neces- 
sary by  just  2'60  days.  But  260  days  are  equal  to  13  uinals;  therefore 
we  must  increase  9.15.6.0.1  by  13  uinals.  This  gives  us  the  number 
9.15.6.13.1.  Keducing  this  to  units  of  the  first  order  and  solving  for 
the  terminal  date,  the  date  reached  will  be  7  Imix  19  Zip,  which  agrees 
with  the  date  recorded  in  C2  D2.  We  may  conclude,  therefore,  that 
the  uinal  coefficient  in  Cl  should  have  been  13,  instead  of  19  as  recorded. 

Another  error  of  the  same  kind — that  is,  one  which  may  be  detected 
by  inspection — is  shown  in  figiare  84,  B.  Passing  over  glyphs  1,  2, 
and  3,  we  reach  in  glyph  4  the  date  5  Kan  13  Uo.  Compare  the 
upper  half  of  4  with  figure  16,/,  and  the  lower  half  with  figure  19,  h,  c. 
The  coefficient  of  the  month  sign  is  very  clearly  13,  which  represents 
an  impossible  condition  when  used  to  indicate  the  position  of  a  day 
whose  name  is  Kan;  for,  according  to  Table  VII,  the  only  positions 
which  the  day  Kan  can  ever  occupy  in  an}"  division  of  the  year 
are  2,  7,  12,  and  17.  Hence,  it  is  evident  that  we  have  detected  an 
error  in  this  text  before  proceeding  with  the  calculations  indicated. 
Let  us  endeavor  to  ascertain  the  coefficient  which  should  have  been 
used  with  the  month  sign  in  glyph  4  instead  of  the  13  actually  recorded. 
These  glyphs  present  seemingly  a  regular  Secondary  Series,  the  start- 
ing point  being  given  in  1  and  2,  the  number  in  3,  and  the  terminal 
date  in  4.  Counting  this  number  3.4  forward  from  the  starting 
point,  6  Ahau  13  Kayab,  the  terminal  date  reached  will  be  6  Kan 
12  TJo.  Comparing  this  with  the  terminal  date  actually  recorded, 
we  find  that  the  two  agree  except  for  the  month  coefficient.  But 
since  the  date  recorded  represents  an  impossible  condition,  as  we 


1  For  a  seeming  exception  to  this  statement,  in  the  codices,  see  p.  110,  footnote  1. 


MOELEY]      IlsrTEODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  247 


have  shown,  we  are  justified  m  assuming  that  the  month  coellicieiit 
which  should  have  been  used  in  glyph  4  was  12,  instead  of  13.  In 
other  words,  the  craftsman  to  whom  the  sculpturing  of  this  inscrip- 
tion was  intrusted  engraved  here  3  dots  instead  of  2  dots,  and  1  orna- 
mental crescent,  which,  together  with  the  2  bars  present,  would  liave 
given  the  month  coefficient  determined  by  calculation,  12.  An  error 
of  this  kind  might  occur  very  easily  and  indeed  in  many  cases  may 
be  apparent  rather  than  real,  being  due  to  weathering  rather  than  to 
a  mistake  in  the  original  text. 

Some  errors  in  the  inscriptions,  however,  can  not  be  detected  by 
inspection,  and  develop  only  after  the  calculations  indicated  hav(^- 
been  performed,  and  the  results  are  found  to  disagree  with  the  glyphs 
recorded.  Errors  of  this  kind  constitute  the  second  class  mentioned 
above.  A  case  in  point  is  the  Initial  Series  on  the  west  side  of  St(4a 
E  at  Quirigua,  figured  in  plate  24,  A.  In  this  text  the  Initial-series 
number  recorded  in  A4-A6  is  very  clearly  9.14.12.4.17,  and  the  ter- 
minal date  in  B6-B8b  is  equally  clearly  12  Caban  5  Kayab.  Now,  if 
this  number  9.14.12.4.17  is  reduced  to  units  of  the  first  order  and  is 
counted  forward  from  the  same  starting  point  as  practically  all  oihvr 
Initial  Series,  the  terminal  date  reached  will  be  3  Caban  10  Kayab, 
not  12  Caban  6  Kayab,  as  recorded.  Moreover,  if  the  same  number 
is  counted  forward  from  the  date  4  Ahau  8  Zotz,  which  may  have 
been  another  starting  point  for  Initial  Series,  as  we  have  seen,  the 
terminal  date  reached  will  be  3  Caban  10  Zip,  not  12  Caban  5  Kayab, 
as  recorded.  The  inference  is  obvious,  therefore,  that  there  is  some 
error  in  this  text,  since  the  number  recorded  can  not  be  made  to 
reach  the  date  recorded.  An  error  of  this  kind  is  difficult  to  detect, 
because  there  is  no  indication  in  the  text  as  to  which  glyph  is  the  one 
at  fault.  The  first  assumption  the  writer  makes  in  such  cases  is 
that  the  date  is  correct  and  that  the  error  is  in  one  of  the  period- 
glyph  coefficients.  Referring  to  Goodman's  Table,  it  will  be  found 
that  the  date  12  Caban  5  Kayab  occurred  at  the  following  positions 
in  Cycle  9  of  the  Long  Count : 

9.  1.  9.11.17    12  Caban  5  Kayab 

9.  4.  2.  6.17    12  Caban  5  Kayab 

9.  6.15.  1.17    12  Caban  5  Kayab 

9.  9.  7.14.17    12  Caban  5  Kayab 

9.12.  0.  9.17    12  Caban  5  Kayab 

9.14.13.  4.17    12  Caban  5  Kayab 

9.17.  •  5.17.17    12  Caban  5  Kayab 

9.19.18.12.17  12  Caban  5  Kayab 
An  examination  of  these  values  will  show  that  the  sixth  in  the  list, 
9.14.13.4.17,  is  very  close  to  the  number  recorded  in  our  text, 
9.14.12.4.17.  Indeed,  the  only  difference  between  the  two  is  that 
the  former  has  13  tuns  while  the  latter  has  only  12.  The  similarity 
between  these  two  numbers  is  otherwise  so  close  and  the  error  in  this 


248 


BUREAU  OF  AMERICAl^  ETHNOLOGY 


[boll.  57 


event  would  be  so  slight — the  record  of  2  dots  and  1  ornamental 
crescent  instead  of  3  dots — that  the -conclusion  is  almost  inevitable 
that  the  error  here  is  in  the  tun  coefficient,  12  having  been  recorded 
instead  of  13.  In  this  particular  case  the  Secondary  Series  and  the 
Period-ending  date,  -which  follow  the  Initial-series  number 
9.14.12.4.17,  prove  that  the  above  reading  of  13  tuns  for  the  12 
actually  recorded  is  the  one  correction  needed  to  rectify  the  error  in 
this  text. 

Another  example  indicating  an  error  which  can  not  be  detected  by 
inspection  is  shown  in  figure  84,  C.  In  glyphs  1  and  2  appears  the 
date  8  Eznab  16  XJo  (compare  glyph  1  with  fig.  16,  c'',  and  glyph  2 
with  fig.  19,  h,  c).  In  glyph  3  follows  a  number  consisting  of  17  kins 
and  4  uinals  (4.17).  Finally,  in  glyphs  4  and  5  is  recorded  the  date 
2  Men  13  Yaxkin  (compare  glyph  4  with  fig.  16,  y,  and  glyph  5  with 
fig.  19,  Z:,  Z).  This  has  every  appearance  of  being  a  Secondary  Series, 
of  which  8  Eznab  16  TJo  is  the  starting  point,  4.17,  the  number  to  be 
counted,  and  2  Men  13  Yaxkin  the  terminal  date.  Reducing  4.17  to 
units  of  the  first  order  and  counting  it  forward  from  the  start- 
ing point  indicated,  the  terminal  date  reached  will  be  1  Men  13 
Yaxkin.  This  differs  from  the  terminal  date  recorded  in  glyphs 
4  and  5  in  having  a  day  coefficient  of  1  instead  of  2.  Since  this 
involves  but  a  very  slight  change  in  the  original  text,  we  are  probably 
justified  in  assuming  that  the  day  coefficient  in  glyph  4  should  have 
been  1  instead  of  2,  as  recorded. 

One  more  example  will  suffice  to  show  the  kind  of  errors  usually 
encountered  in  the  inscriptions.  In  plate  26  is  figured  the  Initial 
Series  from  Stela  N  at  Copan.  The  introducing  glyph  appears  in  Al 
and  is  followed  by  the  Initial-series  number  9.16.10.0.0  in  A2-A6, 
all  the  coefficients  of  which  are  unusually  clear.  Reducing  this  to 
units  of  the  first  order  and  solving  for  the  terminal  date,  the  date 
reached  will  be  1  Ahau  3  Zip.  This  agrees  with  the  terminal  date 
recorded  in  A7-A15  except  for  the  month  coefficient,  which  is  8  in 
the  text  instead  of  3,  as  determined  by  calculation.  Assuming  that 
the  date  recorded  is  correct  and  that  the  error  is  in  the  coefficient  of 
the  period  glyphs,  the  next  step  is  to  find  the  positions  in  Cycle  9  at 
which  the  date  1  Ahau  8  Zip  occurred.  Referring  to  Goodman's 
Tables,  these  will  be  found  to  be : 

9.  0.  8.11.0  1  Ahau  8  Zip 

9.  3.  1.  6.0  1  Ahau  8  Zip 

9.  5.14.  1.0  1  Akau  8  Zip 

9.  8.  6.14.0  1  Ahau  8  Zip 

9.10.19.  9.0  1  Akau  8  Zip 

9.13.12.  4.0  1  Akau  8  Zip 

9.16.  4.17.0  1  Akau  8  Zip 

9.18.17.12.0  1  Akau  8  Zip 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57 


PLATE  26 


INITIAL  SERIES  ON  STELA  N,  COPAN,  SHOWING 
ERROR  IN   MONTH  COEFFICIENT 


MORLET]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  249 

The  number  in  the  above  Hst  coming  nearest  to  the  number  recorded 
in  this  text  (9.16.10.0.0)  is  the  next  to  the  last,  9.16.4.17.0.  But  in 
order  to  r^ach  this  value  of  the  date  1  Ahau  8  Zip  (9.16.4.17.0)  with 
the  number  actually  recorded,  two  considerable  changes  in  it  are  first 
necessary,  (1)  replacing  the  10  tuns  in  A4  by  4  tuns,  that  is,  changing 

2  bars  to  4  dots,  and  (2)  replacing  0  uinals  in  A5  by  17  uinals,  that  is, 
changing  the  0  sign  to  3  bars  and  2  dots.  But  these  changes  involve 
a  very  considerable  alteration  of  the  original,  and  it  seems  highly 
improbable,  therefore,  that  the  date  here  intended  was  9.16.4.17.0 
1  Ahau  8  Zip.  Moreover,  as  any  other  number  in  the  above  list 
involves  at  least  three  changes  of  the  number  recorded  in  order  to 
reach  1  Ahau  8  Zip,  we  are  forced  to  the  conclusion  that  the  error 
must  be  in  the  terminal  date,  not  in  one  of  the  coefficients  of  the 
period  glyphs.  Let  us  therefore  assume  in  our  next  trial  that 
the  Initial-series  number  is  correct  as  it  stands,  and  that  the  error 
lies  somewhere  in  the  terminal  date.  But  the  terminal  date  reached 
in  counting  9.16.10.0.0  forward  in  the  Long  Count  will  be  1  Ahau 

3  Zip,  as  we  have  seen  on  the  preceding  page,  and  this  date  differs 
from  the  terminal  date  recorded  by  5 — 1  bar  in  the  month  coefficient. 
It  would  seem  probable,  therefore,  that  the  bar  to  the  left  of  the  month 
sign  in  Al5  should  have  been  omitted,  in  which  case  the  text  would 
correctly  record  the  date  9.16.10.0.0  1  Ahau  3  Zip. 

The  student  will  note  that  in  all  the  examples  above  given  the 
errors  have  been  in  the  numerical  coefficients,  and  not  in  the  signs 
to  which  they  are  attached;  in  other  words,  that  although  the 
numerals  are  sometimes  incorrectly  recorded,  the  period,  day,  and 
month  glyphs  never  are. 

Throughout  the  inscriptions,  the  exceptions  to  this  rule  are  so 
very  rare  that  the 'beginner  is  strongly  advised  to  disregard  them  al- 
together, and  to  assume  when  he  finds  an  incorrect  text  that  the  error 
is  in  one  of  the  numerical  coefficients.  It  should  be  remembered 
also  in  this  connection  that  errors  in  the  inscriptions  are  exceed- 
ingly rare,  and  a  glyph  must  not  be  condemned  as  incorrect  until 
every  effort  has  been  made  to  explain  it  in  some  other  way. 

This  concludes  the  presentation  of  texts  from  the  inscriptions. 
The  student  will  have  noted  in  the  foregoing  examples,  as  was  stated 
in  Chapter  II,  that  practically  the  only  advances  made  looking  toward 
the  decipherment  of  the  glyphs  have  been  on  the  chronological  side. 
It  is  now  generally  admitted  that  the  relative  ages  ^  of  most  Maya 
monuments  can  be  determined  from  the  dates  recorded  upon  them, 
and  that  the  final  date  in  almost  every  inscription  indioates  the  time 
at  or  near  which  the  monument  bearing  it  was  erected,  or  at  least 
formally  dedicated.    The  writer  has  endeavored  to  show,  moreover. 


1  That  is,  the  age  of  one  compared  with  the  age  of  another,  without  reference  to  their  actual  age  as 
expressed  in  terms  of  our  own  chronology. 


250 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


that  many,  if  indeed  not  most,  of  the  monuments,  were  ''time  mark- 
ers'' or  ''period  stones,"  in  every  way  similar  to  the  "period  stones" 
which  the  northern  Maya  are  known  to  ^  have  erected  at.  regularly 
recurring  periods.  That  the  period  which  was  used  as  this  chrono- 
logical unit  may  have  varied  in  different  localities  and  at  different 
epochs  is  not  at  all  improbable.  The  northern  Maya  at  the  time  of 
the  Spanish  Conquest  erected  a  "period  stone"  every  katun,  while 
the  evidence  presented  in  the  foregoing  texts,  particularly  those  from 
Quirigua  and  Copan,  indicates  that  the  chronological  unit  in  these 
two  cities  at  least  was  the  hotun,  or  quarter-katun  period.  What- 
ever may  have  been  the  chronological  unit  used,  the  writer  beheves 
that  the  best  explanation  for  the  monuments  found  so  abundantly 
in  the  Maya  area  is  that  they  were  "period  stones,"  erected  to  com- 
memorate or  mark  the  close  of  successive  periods. 

That  we  have  succeeded  in  deciphering,  up  to  the  present  time,  only 
the  calendric  parts  of  the  inscriptions,  the  chronological  skeleton 
of  Maya  history  as  it  were,  stripped  of  the  events  which  would  vitalize 
it,  should  not  discourage  the  student  nor  lead  him  to  minimize  the 
importance  of  that  which  is  already  gained.  Thirty  years  ago  the 
Maya  inscriptions  were  a  sealed  book,  yet  to-day  we  read  in  the 
glyphic  writing  the  rise  and  fall  of  the  several  cities  in  relation  to  one 
another,  and  follow  the  course  of  Maya  development  even  though  we 
can  not  yet  fill  in  the  accompanying  background.  Future  researches, 
we  may  hope,  will  reconstruct  this  background  from  the  undeciphered 
glyphs,  and  will  reveal  the  events  of  Maya  history  which  alone  can 
give  the  corresponding  chronology  a  human  interest. 


1  See  Chapter  II  for  the  discussion  of  this  point  and  the  quotations  from  contemporary  authorities,  both 
Spanish  and  native,  on  which  the  above  statement  is  based. 


Chapter  VI 
THE  CODICES 

this  subject  will  be  taken  up-first. 

Texts  Eecobding  Tonalamatls 

Tbe  ion.Ur.au,  or  2e0-day  P-od  as  roprese^^^^^^ 
usually  divided  into  five  parts  of  ^2  days  J^^^^ 

n.atls  of  four  parts,       ^-«re  ,ot  at  Tuncommon.  These 
parts,  each  containing  26  days,  are  no 

designated  by  (D  and  (2).  ,,a„allv  4  5,  or  10,  shows  the 

The  number  of  the  day  sig^?;"^/^^\'''"f;^ .  d^ded    Every  red 
number  of  parts  into  which  .t"-l^^^^^^^^  ^.to,  a 

number  in  (2)  is  used  once  with  ^I'^.  oJ  tlTuA  numbers  in  (3) 
day  which  is  reached  ^-;2TZ.  ZMhjW  and  (2).  The 
fo/ward  from  another  of  the  f^J^  ^^^^^^d;^^  I  ,\„dying  the  Maya 
most  important  point  for  the  f  "f  enWa^^  JJ^^  ,.^d 
tonalamatl  is  the  f-^^^damental  difference  be^  ^^^^ 
numbers  and  the  ^ack  numbers    The  torm  ^^^^ 

coefiicients,  and  togeth-  -^^^^^^^^^^  S  tonalamatl.  The  bla«k 
begin  the  di--''-/tnrd  Ireriuslvely  iim.  co«.fe«,  which  show 

tonalamatl  is  divided.   _  ■  — - 

^^^^^^^^^^^^^^ 


252 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


Most  of  the  numbers,  that  is  (2)  and  (3),  in  the  tonalamatl  are 
presented  in  a  horizontal  row  across  the  page  or  pages  ^  of  the  manu- 
script, the  red  alternating  with  the  black.  In  some  instances,  how- 
ever, the  numbers  appear  in  a  vertical  column  or  pair  of  columns, 
though  in  this  case  also  the  same  alternation  in  color  is  to  be  ob- 
served. More  rarely  the  numbers  are  scattered  over  the  page  indis- 
criminately, seemingly  without  fixed  order  or  arrangement. 

It  will  be  noticed  in  each  of  the  tonalamatls  given  in  the  following 
examples  that  the  record  is  greatly  abbreviated  or  skeletonized.  In 
the  first  place,  we  see  no  month  signs,  and  consequently  the  days 
recorded  are  not  shown  to  have  had  any  fixed  positions  in  the  year. 
Furthermore,  since  the  year  positions  of  the  days  are  not  fixed,  any 
day  could  recur  at  intervals  of  eveiy  260  days,  or,  in  other  words, 
any  tonalamatl  mth  the  divisions  pecuHar  to  it  could  be  used  in 
endless  repetition  throughout  time,  commencing  anew  every  260 
days,  regardless  of  the  positions  of  these  days  in  succeeding  years. 
Nor  is  this  omission  the  only  abbreviation  noticed  in  the  presentation 
of  the  tonalamatl.  Although  every  tonalamatl  contained  260  days, 
only  the  days  commencing  its  divisions  and  subdivisions  appear  in 
the  record,  and  even  these  are  represented,  in  an  abbreviated  form. 
For  example,  instead  of  repeating  the  numerical  coefficients  with  each 
of  the  day  signs  in  (1),  the  coefficient  was  written  once  above  the 
column  of  day  signs,  and  in  this  position  was  regarded  as  belong- 
ing to  each  of  the  different  day  signs  in  turn.  It  follows  from  this 
fact  that  all  the  main  divisions  of  the  tonalamatl  begin  with  days  the 
coefficients  of  which  are  the  same.  Concerning  the  beginning  days 
of  the  subdivisions,  a  still  greater  abbreviation  is  to  be  noted.  The 
day  signs  are  not  shown  at  all,  and  only  their  numerical  coefficients 
appear  in  the  record.  The  economy  of  space  resulting  from  the 
above  abbreviations  in  writing  the  days  will  appear  very  clearly  in 
the  texts  to  follow. 

In  reading  tonalamatls  the  first  point  to  be  determined  is  the  name 
of  the  day  with  which  the  tonalamatl  began.    This  wiU  be  found  thus: 

Rule  1.  To  find  the  beginning  day  of  a  tonalamatl,  prefix  the  first  . 
red  number,  which  will  usually  be  found  immediately  above  the  col- 
umn of  the  day  signs,  to  the  uppermost  ^  day  sign  in  the  column. 

From  this  day  as  a  starting  point,  the  first  black  number  in  the  text 
is  to  be  counted  forward;  and  the  coefficient  of  the  day  reached  wiU 
be  the  second  red  number  in  the  text.  As  stated  above,  the  day 
signs  of  the  beginning  days  of  the  subdivisions  are  always  omitted. 
From  the  second  red  number,  which,  as  we  have  seen,  is  the  coeffi- 

1  The  codices  are  folded  like  a  screen  or  fan,  and  when  opened  form  a  continuous  strip  sometimes  several 
yards  in  length.  As  will  appear  later,  in  many  eases  one  tonalamatl  runs  across  several  pages  of  the 
manuscript. 

2  If  there  should  be  two  or  more,  columns  of  day  signs  the  topmost  sign  of  the  left-hand  column  is  to  be 
read  first. 


MOELEY]      INTRODUCTION  TO  STUDY   OJ^^  MAYA  TilEKOGLYPHS  253 

cient  of  the  beginning  day  of  the  second,  subdivision  of  the  first  divi- 
sion, the  second  Hack  number  is  to  be  counted  forward  in  order  to 
reach  the  third  red  number,  which  is  the  coefficient  of  the  day  begin- 
ning the  third  subdivision  of  the  first  division.  This  operation  is 
continued  until  the  last  black  number  has  been  counted  forward  from 
the  red  number  just  preceding  it  and  the  last  red  number  has  been 
reached. 

This  last  red  number  will  be  found  to  be  the  same  as  the  first  red 
number,  and  the  day  which  the  count  will  have  reached  will  be  shown 
by  the  first  red  number  (or  the  last,  since  the  two  are  identical)  used 
with  the  second  day  sign  in  the  column.  And  this  latter  day  will  be 
the  beginning  day  of  the  second  division  of  the  tonalamatl.  From 
this  day  the  count  proceeds  as  before.  The  black  numbers  are 
added  to  the  red  numbers  immediately  preceding  them  in  each  case, 
until  the  last  red  number  is  reached,  which,  together  with  the  third 
day  sign  in  the  column,  forms  the  beginning  day  of  the  third  division 
of  the  tonalamatl.  After  this  operation  has  been  repeated  until  the 
last  red  number  in  the  last  division  of  the  tonalamatl  has  been 
reached — that  is,  the  260th  day — the  count  will  be  found  to  have 
reentered  itself,  or  in  other  words,  the  day  reached  by  counting  for- 
ward the  last  black  number  of  the  last  division  will  be  the  same  as 
the  beginning  day  of  the  tonalamatl. 

It  follows  from  the  foregoing  that  the  sum  of  all  the  black  numbers 
multiplied  by  the  number  of  day  signs  in  the  column — the  number 
of  main  divisions  in  the  tonalamatl — will  equal  exactly  260.  If  any 
tonalamatl  fails  to  give  260  as  the  result  of  this  test,  it  may  be  regarded 
as  incorrect  or  irregular. 

The  foregoing  material  may  be  reduced  to  the  following: 

Rule  2.  To  find  the  coefficients  of  the  beginning  days  of  succeeding 
divisions  and  subdivisions  of  the  tonalamatl,  add  the  black  numbers 
to  the  red  numbers  immediately  preceding  them  in  each  case,  and, 
after  subtracting  all  the  multiples  of  13  possible,  the  resulting  num- 
ber wiU  be  the  coefficient  of  the  beginning  day  desired. 

Rule  3.  To  find  the  day  signs  of  the  beginning  days  of  the  suc- 
ceeding divisions  and  subdivisions  of  the  tonalamatl,  count  forward 
y  in  Table  I  the  black  number  from  the  day  sign  of  the  beginning  day 

of  the  preceding  division  or  subdivision,  and  the  day  name  reached 
in  Table  I  will  be  the  day  sign  desired.  If  it  is  at  the  beginning  of  one 
of  the  main  divisions  of  the  tonalamatl,  the  day  sign  reached  will  be 
found  to  be  recorded  in  the  column  of  day  signs,  but  if  at  the  begin- 
ning of  a  subdivision  it  will  be  unexpressed. 

To  these  the  test  rule  above  given  may  be  added: 

Rule  4-  The  sum  of  all  the  black  numbers  multiplied  by  the 
number  of  day  signs  in  the  column  of  day  signs  wiU  equal  exactly  260 
if  the  tonalamatl  is  perfectly  regular  and  correct. 


254 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


In  plate  27  is  figured  page  12  of  the  Dresden  Codex.  It  will  be 
noted  that  this  page  is  divided  into  three  parts  by  red  division  lines ; 
after  the  general  practice  these  have  been  designated  a,  h,  and  c,  a 
being  apphed  to  the  upper  part,  h  to  the  middle  part,  and  c  to  the 
lower  part.  Thus  ''Dresden  12b"  designates  the  middle  part  of 
page  12  of  the  Dresden  Codex,  and  ''Dresden  15c"  the  lower  part  of 
page  15  of  the  same  manuscript.  Some  of  the  pages  of  the  codices 
are  divided  into  four  parts,  or  again,  into  two,  and  some  are  not 
divided  at  aU.  The  same  description  applies  in  all  cases,  the  parts 
being  lettered  from  top  to  bottom  in  the  same  manner  throughout. 

The  first  tonalamatl  presented  will  be  that  shown  in  Dresden  12b 
(see  the  middle  division  in  pi.  27).  The  student  wiU  readily  recog- 
nize the  three  essential  parts  mentioned  on  page  251:  (1)  The  column 
of  day  signs,  (2)  the  red  numbers,  and  (3)  the  black  numbers.  Since 
there  are  five  day  signs  in  the  column  at  the  left  of  the  page,  it  is 
evident  that  this  tonalamatl  has  five  main  divisions.  The  first  point 
to  establish  is  the  day  with  which  this  tonalamatl  commenced. 
According  to  rule  1  (p.  252)  this  will  be  found  by  prefixing  the  first  red 
number  to  the  topmost  day  sign  in  the  column.  The  first  red  number 
in  Dresden  12b  stands  in  the  regular  position  (above  the  column  of 
day  signs),  and  is  very  clearly  1,  that  is,  one  red  dot.  A  comparison 
of  the  topmost  day  sign  in  this  column  with  the  forms  of  the  day  signs 
in  figure  17  will  show  that  the  day  sign  here  recorded  is  Ix  (see  fig. 
17,  t),  and  the  opening  day  of  this  tonalamatl  wiU  be,  therefore,  1  Ix. 
The  next  step  is  to  find  the  beginning  days  of  the  succeeding  subdi- 
visions of  the  first  main  division  of  the  tonalamatl,  which,  as  we  have 
just  seen,  commenced  with  the  day  1  Ix.  According  to  rtde  2  (p. 
253),  the  first  black  number — in  this  case  13,  just  to  the  right  of  and 
slightly  below  the  day  sign  Ix — is  to  be  added  to  the  red  number 
immediately  preceding  it— in  this'  case  1 — in  order  to  give  the  coeffi- 
cient of  the  day  beginning  the  next  subdivision,  all  13s  possible 
being  first  deducted  from  the  resulting  number.  Fm-thermore,  this 
coefiicient  will  be  the  red  number  next  following  the  black  number. 

Applying  this  rule  to  the  present  case,  we  have: 

1  (first  red  number)  +  13  (next  black  number)  =  14.  Deducting  all 
the  13s  possible,  we  have  left  1  (14-13)  as  the  coefficient  of  the 
day  beginning  the  next  subdivision  of  the  tonalamatl.  This  number 
1  will  be  foimd  as  the  red  number  immediately  following  the  first 
black  number,  13.  To  find  the  corresponding  day  sign,  we  must 
turn  to  rule  3  (p.  253)  and  count  forward  in  Table  I  this  same  black 
number,  13,  from  the  preceding  day  sign,  in  this  case  Ix.  The  day 
sign  reached  will  be  Manik.  But  since  this  day  begins  only  a  suh- 
division  in  this  tonalamatl,  not  one  of  the  main  divisions,  its  day 
sign  will  not  be  recorded,  and  we  have,  therefore,  the  day  1  Manik, 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57  PLATE 


PAGE  12  OF  THE  DRESDEN  CODEX,  SHOWING 

T-rkMAi  AMATI  Q  IM  Al  I    THRFF  DIVISIONS 


MOELBY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  255 


of  which  the  1  is  expressed  by  the  second  red  number  and  the  name 
part  Manik  only  indicated  by  the  calculations. 

The  beginning  day  of  the  next  subdivision  of  the  tonalamatl  may 
now  be  calculated  from  the  day  1  Manik  by  means  of  rules  2.  and  3 
(p.  253) .  Before  proceeding  with  the  calculation  incident  to  this  step 
it  will  be  necessary  first  to  examine  the  next  black  number  in  our 
tonalamatl.  This  will  be  found  to  be  composed  of  this  sign  (*), 
to  which  6  (1  bar  and  1  dot)  has  been  affixed.  It  was  explained  * 
on  page  92  that  in  representing  tonalamatls  the  Maya  had  to  have  a 
sign  which  by  itself  would  signify  the  number  20,  since  numeration  by 
position  was  impossible.  This  special  character  for  the  number  20 
was  given  in  figure  45,  and  a  comparison  of  it  with  the  sign  here  under 
discussion  will  show  that  the  two  are  identical.  But  in  the  present 
example  the  number  6  is  attached  to  this  sign  thus:  (**),  C^)^ 
and  the  whole  number  is  to  be  read  20  +  6  =  26.  This  ** 
number,  as  we  have  seen  in  Chapter  IV,  would  ordinarily  have  been 
:  written  thus  (f) :  1  unit  of  the  second  order  (20  units  of  the  first 
t  order)  +6  units  of  the  first  order  =  26.  As  explained  on  page 
92,  however,  numeration  by  position — that  is,  columns  of  units — 
was  impossible  in  the  tonalamatls,  in  which  many  of  the  numbers 
appear  in  a  horizontal  row,  consequently  some  character  had  to  be 
devised  which  by  itself  would  stand  for  the  number  20. 

Returning  to  our  text,  we  find  that  the  '^next  black  number"  is 
26  (20  +  6),  and  this  is  to  be  added  to  the  red  number  1  next  pre- 
ceding it,  which,  as  we  have  seen,  is  an  abbreviation  for  the  day 
1  Manik  (see  rule  2,  p.  253).  Adding  26  to  1  gives  27,  and  deducting 
all  the  13s  possible,  namely,  two,  we  have  left  1  (27  —  26);  this  num- 
ber 1,  which  is  the  coefficient  of  the  beginning  day  of  the  next  subdi- 
vision, will  be  found  recorded  just  to  the  right  of  the  black  26. 

The  day  sign  corresponding  to  this  coefficient  1  will  be  found  by 
counting  forward  26  in  Table  I  from  the  day  name  Manik.  This  will 
give  the  day  name  Ben,  and  1  Ben  will  be,  therefore,  the  beginning 
day  of  the  next  subdivision  (the  third  subdivision  of  the  first  main 
division). 

The  next  black  number  in  our  text  is  13,  and  proceeding  as  before, 
this  is  to  be  added  to  the  red  number  next  preceding  it,  1,  the  abbre- 
viation for  1  Ben.  Adding  13  to  1  we  have  14,  and  deducting  all  the 
23s  possible,  we  obtain  1  again  (14-13),  which  is  recorded  just  to 
the  right  of  the  black  13  (rule  2,  p.  253).^  Counting  forward  13  in 
Table  I  from  the  day  name  Ben,  the  day  name  reached  will  be  Cimi, 
and  the  day  1  Cimi  will  be  the  beginning  day  of  the  next  part  of  the 
tonalamatl.  But  since  13  is  the  last  black  number,  we  should  have 
reached  in  1  Cimi  the  beginning  day  of  the  second  main  division  of 


1  In  the  original  this  last  red  dot  has  disappeared.  The  writer  has  inserted  it  here  to  avoid  confusing 
the  beginner  in  his  first  acquaintance  with  a  tonalamatl. 


256 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


the  tonalamatl  (see  p.  253),  and  this  is  found  to  be  the  case,  since 
the  day  sign  Cimi  is  the  second  in  the  column  of  day  signs  to  the  left. 
Compare  this  form  with  figure  17,  ^,  j.  The  day  recorded  is  therefore 
1  Cimi. 

The  first  division  of  the  tonalamatl  under  discussion  is  subdivided, 
therefore,  into  three  parts,  the  first  part  commencing  with  the  day 
1  Ix,  containing  13  days;  the  second  commencing  with  the  day  1 
Manik,  containing  26  days ;  and  the  third  commencing  with  the  day 
1  Ben,  containing  13  days. 

The  second  division  of  the  tonalamatl  commences  with  the  day 
1  Cimi,  as  we  have  seen  above,  and  adding  to  this  the  first  black 
number,  13,  as  before,  according  to  rules  2  and  3  (p.  253),  the  begin- 
ning day  of  the  next  subdivision  will  be  found  to  be  1  Cauac.  Of 
this,  however,  only  the  1  is  declared  (see  to  the  right  of  the  black  13). 
Adding  the  next  black  number,  26,  to  this  day,  according  to  the  above 
rules  the  beginning  day  of  the  next  subdivision  will  be  found  to  be 
1  Chicchan.  Of  this,  however,  the  1  again  is  the  only  part  declared. 
Adding  the  next  and  last  black  number,  13,  to  this  day,  1  Chicchan, 
according  to  the  rules  just  mentiori^d  the  beginning  day  of  the  next, 
or  third,  main  division  will  be  found  to  be  1  Eznab.  Compare  the 
third  day  sign  in  the  column  of  day  signs  with  the  form  for  Eznab  in 
figure  17,  z,  a' .  The  second  division  of  this  tonalamatl  contains, 
therefore,  three  parts:  The  first,  commencing  with  the  day  1  Cimi, 
containing  13  days;  the  second,  commencing  with  the  day  1  Cauac, 
containing  26  days;  and  the  third,  commencing  with  the  day  1 
Chicchan,  containing  13  days. 

Similarly  the  third  division,  commencing  with  the  day  1  Eznab, 
could  be  shown  to  have  three  parts,  of  13,  26,  and  13  days  each,  com- 
mencing with  the  day  1  Eznab,  1  Chuen,  and  1  Caban,  respectively. 
It  could  be  shown,  also,  that  the  fourth  division  commenced  with  tho 
day  1  Oc  (compare  the  fourth  sign  in  the  column  of  day  signs  with 
figure  17,  o),  and,  further,  that  it  had  three  subdivisions  containing 
13,  26,  and  13  days  each,  commencing  with  the  days  1  Oc,  1  Akbal, 
and  1  Muluc,  respectively.  Finally,  the  fifth  and  last  division  of  the 
tonalamatl  will  commence  with  the  day  1  Ik.  Compare  the  last  day 
sign  in  the  column  of  day  signs  with  figure  17,  c,  d\  and  its  three 
subdivisions  of  13,  26,  and  13  days  each  with  the  days  1  Ik,  1  Men, 
and  1  Imix,  respectively.  The  student  will  note  also  that  when  the 
last  black  number,  13,  has  been  added  to  the  beginning  day  of  the 
last  subdivision  of  the  last  division,  the  day  reached  will  be  1  Ix,  the 
day  with  which  the  tonalamatl  commenced.  This  period  is  con- 
tinuous, therefore,  reentering  itself  immediately  on  its  conclusion  and 
commencing  anew. 


MORLBT]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEEOGLYPIIS  257 


There  follows  below  an  outline  ^  of  this  particular  tonalamatl: 


1st  Division 

2(i  Division 

3(i  Division 

4th  Division 

5th  Division 

1st  part,  13  days,  beginning 

with  day  

1  Ix 

1  Cimi 

1  Sziial) 

1  Oc 

1  Ik 

2d  part,  26  days,  beginning 

with,  day  

1  Manik 

1  Cauac 

1  Cliuen 

1  Akbal 

1  Men 

3d  part,  13  days,  beginning 

with  day  

1  Ben 

1  CMcclian 

1  Caban 

1  Muluc 

1  Imix 

Total  number  of  days  

52 

52 

52 

52 

52 

Next  tonalamatl:  1st  Division,  1st  part,  13  days,  beginning  with  the  day  1  Ix,  etc. 


We  may  now  apply  rule  4  (p.  253)  as  a  test  to  this  tonalamatl. 
Multiplying  the  sum  of  all  the  black  numbers,  13  +  26  +  13  =  52,  by 
the  number  of  day  signs  in  the  column  of  day  signs,  5,  we  obtain  260 
(52  X  5),  which  proves  that  this  tonalamatl  is  regular  and  correct. 

The  student  will  note  in  the  middle  division  of  plate  27  that  the 
pictures  are  so  arranged  that  one  picture  stands  under  the  first  sub- 
divisions of  all  the  divisions,  the  second  picture  under  the  second 
subdivisions,  and  the  third  under  the  third  subdivisions.  It  has 
been  conjectured  that  these  pictures  represent  the  gods  who  were  the 
patrons  or  guardians  of  the  subdivisions  of  the  tonalamatls,  under 
which  each  appears.  In  the  present  case  the  first  god  pictured  is 
the  Death  Deity,  God  A  (see  fig.  3) .  Note  the  fleshless  lower  jaw,  the 
trimcated  nose,  and  the  vertebrae.  The  second  deity  is  unknown, 
but  the  third  is  again  the  Death  God,  having  the  same  characteristics 
as  the  god  in  the  first  picture.  The  cloak  worn  by  this  deity  in  the 
third  picture  shows  the  crossbones,  which  would  seem  to  have  been 
an  emblem  of  death  among  the  Maya  as  among  us.  The  glyphs 
above  these  pictures  probably  explain  the  nature  of  the  periods  to 
which  they  refer,  or  perhaps  the  ceremonies  peculiar  or  appropriate 
to  them.  In  many  cases  the  name  glyphs  of  the  deities  who  appc^ir 
below  them  are  given;  for  example,  in  the  present  text,  the  second 
and  sixth  glyphs  in  the  upper  row  ^  record  in  each  case  the  fact  that 
the  Death  God  is  figured  below. 

The  glyphs  above  the  pictures  offer  one  of  the  most  promising 
problems  in  the  Maya  field.  It  seems  probable,  as  just  explained, 
that  the  four  or  six  glyphs  which  stand  above  each  of  the  pictures  in 
a  tonalamatl  tell  the  meaning  of  the  picture  to  which  they  arc 
appended,  and  any  advances  made,  looking  toward  their  decipher- 
ing, will  lead  to  far-reaching  results  in  the  meaning  of  the  nonnu- 

1  This  and  similar  outlines  which  foUow  are  to  be  read  down  in  columns. 

2  The  fifth  sign  in  the  lower  row  is  also  a  sign  of  the  Death  God  (see  fig.  3).  Note  the  eyelashes,  suggesting 
the  closed  eyes  of  the  dead. 

43508°— Bull.  57—15  17 


258 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[BULL.  57 


merical  and  noncalendric  signs.  In  part  at  least  they  show  the 
name  glyphs  of  the  gods  above  which  they  occur,  and  it  seems  not 
unlikely  that  the  remaining  glyphs  may  refer  to  the  actions  of  the 
deities  who  are  portrayed;  that  is,  to  the  ceremonies  in  which  they 
are  engaged.  More  extended  researches  along  this  line,  however, 
must  be  made  before  this  question  can  be  answered. 

The  next  tonalamatl  to  be  examined  is  that  shown  in  the  lower 
division  of  plate  27,  Dresden  12c.  At  first  sight  this  would  appear 
to  be  another  tonalamatl  of  five  divisions,  like  the  preceding  one, 
but  a  closer  examination  reveals  the  fact  that  the  last  day  sign  in 
the  column  of  day  signs  is  like  the  first,  and  that  consequently  there 
are  only  four  different  signs  denoting  four  divisions.  The  last,  or 
fifth  sign,  like  the  last  red  number  to  which  it  corresponds,  merely 
indicates  that  after  the  260th  day  the  tonalamatl  reenters  itself  and 
commences  anew. 

Prefixing  the  first  red  number,  13,  to  the  first  day  sign,  Chuen  (see 
fig-  17,  2?,  q),  according  to  rule  1  (p.  252),  the  beginning  day  of  the 
tonalamatl  will  be  found  to  be  13  Chuen.  Adding  to  this  the  first 
black  number,  26,  according  to  rules  2  and  3  (p.  253),  the  beginning 
day  of  the  next  subdivision  will  be  foimd  to  be  13  Caban.  Since  this 
day  begins  only  a  subdivision  of  the  tonalamatl,  however,  its  name 
part  Caban  is  omitted,  and  merely  the  coefficient  13  recorded.  Com- 
mencing with  the  day  13  Caban  and  adding  to  it  the  next  black 
number  in  the  text,  again  26,  according  to  rules  2  and  3  (p.  253),  the 
beginning  day  of  the  next  subdivision  will  be  found  to  be  13  Akbal, 
represented  by  its  coefficient  13  only.  Adding  the  last  black  number 
in  the  text,  13,  to  13  Akbal,  according  to  the  rules  just  mentioned, 
the  beginning  day  of  the  next  part  of  the  tonalamatl  will  be  found  to 
be  13  Cib.  And  since  the  black  13  which  gave  this  new  day  is  the 
last  black  number  in  the  text,  the  new  day  13  Cib  will  be  the  begin- 
ning day  of  the  next  or  second  division  of  the  tonalamatl,  and  it  will 
be  recorded  as  the  second  sign  in  the  column  of  day  signs.  Compare 
the  second  day  sign  in  the  column  of  day  signs  with  figure  17,  v,  w. 

Following  the  above  rules,  the  student  will  have  no  difficulty  in 
working  out  the  beginning  days  of  the  remaining  divisions  and  sub- 
divisions of  this  tonalamatl.  These  are  given  below,  though  the 
student  is  urged  to  work  them  out  independently,  using  the  follow- 
ing outline  simply  as  a  check  on  his  work.  Adding  the  last  black 
number,  13,  to  the  beginning  day  of  the  last  subdivision  of  the  last 
division,  13  Eznab,  will  bring  the  count  back  to  the  day  13  Chuen 
with  which  the  tonalamatl  began: 


MOKLET]      INTEODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  259 


1st  Division 

2d  Division 

3d  Division 

4th  Division 

1st  part,  26  days,  beginning 

with  day  

13  Chuen 

13  Cib 

13  Imix 

13  Cimi 

2d  part,  26  days,  beginning 

with  day  

13  Caban 

13  Ik 

13  Manik 

13  Eb 

ou.  pdi  u,  xo   Qays,  Degmning 

with  day  

13  Akbal 

13  Lamat 

13  Ben 

13  Eznab 

Total  number  of  days  

65 

65 

65 

05 

Next  tonalamatl:  1st  division,  1st  part,  26  days,  beginning  with  the  day  13 
Chuen,  etc. 


Applying  the  test  rule  to  this  tonalamatl  (see  rule  4,  p.  253),  we 
have:  26  +  26  +  13  =  65,  the  sum  of  the  black  numbers,  and  4  the 
number  of  the  day  signs  in  the  column  of  day  signs,^  65x4  =  260, 
the  exact  number  of  days  in  a  tonalamatl. 

The  next  tonalamatl  (see  the  upper  part  of  pi.  27,  that  is,  Dresden 
12a)  occupies  only  the  latter  two-thirds  of  the  upper  division,  the 
black  12  and  red  11  being  the  last  black  and  red  numbers,  respec- 
tively, of  another  tonalamatl. 

The  presence  of  10  day  signs  arranged  in  two  parallel  columns  of 
five  each  would  seem  at  first  to  indicate  that  this  is  a  tonalamatl  of 
10  divisions,  but  it  develops  from  the  calculations  that  instead  there 
are  recorded  here  two  tonalamatls  of  five  divisions  each,  the  first 
column  of  day  signs  designating  one  tonalamatl  and  the  second 
another  quite  distinct  therefrom. 

The  first  red  numeral  is  somewhat  effaced,  indeed  all  the  red  has 
disappeared  and  only  the  black  outline  of  the  glyph  remains.  Its 
position,  however,  above  the  column  of  day  signs,  seems  to  indicate 
its  color  and  use,  and  we  are  reasonably  safe  in  stating  that  the  first 
of  the  two  tonalamatls  here  recorded  began  with  the  day  8  Ahau. 
Adding  to  this  the  first  black  number,  27,  the  beginning  day  of  the 
next  subdivision  will  be  found  to  be  9  Manik,  neither  the  coeflicient 
nor  day  sign  of  which  appears  in  the  text.  Assuming  that  the  calcu- 
lation is  correct,  however,  and  adding  the  next  black  number,  25 
(also  out  of  place),  to  this  day,  9  Manik,  the  beginning  day  of  the 
next  part  will  bo  8  Eb.  But  since  25  is  the  last  black  number,  8  Eb 
will  be  the  beginning  day  of  the  next  main  division  and  should  appear 
as  the  second  sign  in  the  first  column  of  day  signs.  Comparison  of 
this  form  with  figure  17,  r,  will  show  that  Eb  is  recorded  in  this  place. 


1  The  last  sign  Chuen,  as  mentioned  above,  is  only  a  repetition  of  the  first  sign,  indicating  that  the 
tonalamatl  has  re-entered  itself. 


260  BUKEAU  OF  AMEEICAN  ETHNOLOGY  [bull.  57 


In  this  manner  all  of  the  beginning  days  could  be  worked  out  as 
below: 


1st  Division 

2d  Division 

3d  Division 

4th  Division 

5th  Division 

1st  part,  27  days,  beginniiig 

8  Ahau 

8Eb 

8  Ean 

8  Cib 

8  Lamat 

2d  part,  25  days,  beginning 

9  Manik 

9  Cauac 

9  Chuen 

9  Akbal 

9  Men 

Total  number  of  days  

52 

52 

52 

52 

52 

The  application,  of  rule  4  (p.  253)  to  this  tonalamatl  gives: 
5  X  52  =  260,  the  exact  number  of  days  in  a  tonalamatl.  As  previously 
explained,  the  second  column  of  day  signs  belongs  to  another  tonala- 
matl, which,  however,  utilized  the  same  red  8  as  the  first  and  the 
same  black  27  and  25  as  the  first.  The  outline  of  this  tonalamatl, 
which  began  with  the  day  8  Oc,  follows: 


1st  Division 

2d  Division 

3d  Division 

4th  Division 

5th  Division 

1st  part,  27  days,  begin- 

ning with  day  

8  Oc 

8  Ik 

8Ix 

8  Cimi 

8  Eznab 

2d  part,  25  days,  begin- 

ning with  day  

9  Caban 

9  Muluc 

9  Imix 

9  Ben 

9  Cliicclian 

Total  number  of  days  in. . . 

52 

52 

52 

52 

52 

The  application  of  rule  4  (p.  253)  to  this  tonalamatl  gives: 
5x52  =  260,  the  exact  number  of  days  in  a  tonalamatl.  It  is  inter- 
estmg  to  note  that  the  above  tonalamatl,  beginning  with  the  day 
8  Oc,  commenced  just  130  days  later  than  the  first  tonalamatl,  which 
began  with  the  day  8  Ahau.  In  other  words,  the  first  of  the  two 
tonalamatls  in  Dresden  12a  wag  just  half  completed  when  the  second 
one  commenced,  and  the  second  half  of  the  first  tonalamatl  began 
with  the  same  day  as  the  first  half  of  the  second  tonalamatl,  and 
vice  versa. 

The  tonalamatl  in  plate  28,  upper  division,  is  from  Dresden  15a, 
and  is  interesting  because  it  illustrates  how  certain  missing  parts 
may  be  filled  in.  The  first  red  number  is  missing  and  we  can  only 
say  that  this  tonalamatl  began  with  some  day  Ahau.  However, 
adding  the  first  black  number,  34,  to  this  day  ?  Ahau,  the  day  reached 
will  be  13  Ix,  of  which  only  13  is  recorded.  Since  13  Ix  was  reached 
by  counting  34  forward  from  the  day  with  which  the  count  must  have 
started,  by  counting  back  34  from  13  Ix  the  starting  point  will  be 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57    PLATE  28 


PAGE  15  OF  THE  DRESDEN  CODEX,  SHOWING 
TONALAMATLS  IN  ALL  THREE  DIVISIONS 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEKOGLYPIIS  261 

found  to  be  5  Ahau,  and  we  may  supply  a  red  bar  above  the  column 
of  the  day  signs.  Adding  the  next  black  number,  18,  to  this  day 
13  Ix,  the  beginning  day  of  the  next  division  will  be  found  to  be  5  Eb, 
which  appears  as  the  second  day  sign  in  the  column  of  day  signs. 

The  last  red  number  is  5,  thus  establishing  as  correct  our  restora- 
tion of  a  red  5  above  the  column  of  day  signs.  From  here  this  tona- 
lamatl  presents  no  unusual  features  and  it  may  be  worked  as  follows: 


1st  Division 

2d  Division 

3d  Division 

4th  Division 

5th  Division 

1st  part,  34  days,  beginning 

with  day   

5  Ah.au 

5Eb 

5  Kan 

6  Cib 

5  Lamat 

2d  part,  18  days,  begiQning 

with  day  

13  Ix 

13  Cimi 

13  Eznab 

13  Oc 

13  Ik 

Total  number  of  days  

52 

52 

52 

52 

52 

Applying  rule  4  (p.  253),  we  have:  5X52  =  260,  the  exact  number 
of  days  in  a  tonalamatl.  The  next  tonalamatl  (see  lower  part  of  pi. 
28,  that  is,  Dresden  15c)  has  10  day  signs  arranged  in  two  parallel 
columns  of  5  each.  This,  at  its  face  value,  would  seem  to  be  divided 
into  10  divisions,  and  the  calculations  confirm  the  results  of  the  pre- 
liminary inspection. 

The  tonalamatl  opens  with  the  day  3  Lamat.  Adding  to  this  the 
first  black  number,  12,  the  day  reached  will  be  2  Ahau,  of  which  only 
the  2  is  recorded  here.  Adding  to  2  Ahau  the  next  black  number, 
14,  the  day  reached  will  be  3  Ix.  And  since  14  is  the  last  black  num- 
ber, this  new  day  will  be  the  beginning  of  the  next  division  in  the 
tonalamatl  and  will  appear  as  the  upper  day  sign  in  the  second  col- 
umn.^ Commencing  with  3  Ix  and  adding  to  it  the  first  black  num- 
ber 12,  the  day  reached  will  be  2  Cimi,  and  adding  to  this  the  next 
black  number,  14,  the  day  reached  will  be  3  Ahau,  which  appears  as 
the  second  glyph  in  the  first  column.  This  same  operation  if  carried 
throughout  will  give  the  following  outline  of  this  tonalamatl : 


1st  Division 

2d  Division 

3d  Division 

4th  Division 

5th  Division 

1st  part,  12  days,  beginning 

3  Lamat 

3Ix 

3  Ahau 

3  Cimi 

3Eb 

2d  part,  14  days,  beginning 

2  Ahau 

2  Cimi 

2Eb 

2  Eznab 

2  Kan 

Total  number  of  days  

26 

26 

26 

26 

26 

1  As  previously  stated,  the  order  of  reading  the  glyphs  in  columns  is  from  left  to  right  and  top  to  bottom. 


262 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


I 


(Concluded) 


OtJU  J-'lViblUll 

5ifV»  "DiviQinn 

OUi-i  JL-'l  V  lOlUJJ. 

3  Eznab 

3  Ean 

3  Oc 

3  Cib 

3  Ik 

2d  part,  14  days,  beginning 

2  Oc 

2Cib 

2  Ik 

2  Lamat 

2Ix 

Total  number  of  days  

26 

26 

26 

26 

26 

Applying  rule  4  (p.  253)  to  this  tonalamatl,  we  have:  10  X  26  =  260, 
the  exact  number  of  days  in  a  tonalamatl. 

The  tonalamatl  which  appears  in  the  middle  part  on  plate  28 — that 
is,  Dresden  15b — extends  over  on  page  16b,  where  there  is  a  black  13 
and  a  red  1.  The  student  will  have  little  difficulty  in  reaching  the 
result  which  follows:  The  last  day  sign  is  the  same  as  the  first,  and 
consequently  this  tonalamatl  is  divided  into  four,  instead  of  five, 
divisions : 


1st  Division 

2d  Division 

3d  Division 

4th  Division 

1st  part,  13  days, 

beginning 

1  Ik 

1  Manik 

lEb 

1  Caban 

2d  part,  31  days. 

beginning 

1  Men 

1  Ahau 

1  CMcclian 

1  Oc 

3d  part,   8  days. 

beginning 

6  Cimi 

6  Cliuen 

6  Cib 

6  Imix 

4th  part,  13  days, 

beginning 

llx 

1  Cauac 

1  Kan 

1  Muluc 

Total  number  of  day 

65 

65 

65 

65 

Applving  rule  4  (p.  253)  to  this  tonalamatl,  we  have:  4x65  =  260, 
the  exact  number  of  days  in  a  tonalamatl.  The  tonalamatls  hereto- 
fore presented  have  all  been  taken  from  the  Dresden  Codex.  The 
following  examples,  however,  have  been  selected  from  tonalamatls  in 
the  Codex  Tro-Cortesianus.  The  student  will  note  that  the  workman- 
ship in  the  latter  manuscript  is  far  inferior  to  that  in  the  Dresden 
Codex.  This  is  particularly  true  with  respect  to  the  execution  of 
the  glyphs. 

The  first  tonalamatl  figured  from  the  Codex  Tro-Cortesianus  (see 
pi.  29)  extends  across  the  middle  part  of  two  pages  (Tro-Cor.  10b, 
lib).  The  four  day  signs  at  the  left  indicate  that  it  is  divided  into 
four  divisions,  of  which  the  first  begms  with  the  day  13  Ik.^  Adding 
to  this  the  first  black  number  9,  the  day  9  Cliuen  is  reached,  and  pro- 
ceeding in  this  manner  the  tonalamatl  may  be  outlmed  as  follows: 


1  The  right-hand  dot  of  the  13  is  effaced. 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57    PLATE  29 


MIDDLE  DIVISIONS  OF  PAGES  10  AND  11  OF  THE  CODEX 
TRO-CORTESIANO,  SHOWING  ONE  TONALAMATL 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57    PLATE  30 


PAGE  113  OF  THE  CODEX  TRO-CORTESIANO,  SHOWING 
TONALAMATLS  IN  THE  LOWER  THREE  SECTIONS 


MOELEY]      INTEODUCTIOlsr  TO  STUDY  OF  MAYA  HIEROGLYPHS  268 


1st  part,   9  days,  beginning 

with  day  

2d   part,   9   days,  beginning 

with  day  

3d  part,  10  days,  beginning 

with  day  

4th  part,  6  days,  beginning 

with  day  

5th  part,  2  days,  beginning 

with  day  

6th  part,  10  days,  beginning 


with  day. 
;h  part,  I 
with  day. 


days. 

beginning 

days. 

be^ 

ginning 

with  day. 
9th  part,   7  days,  beginning 

with  day  

Total  number  of  days  ...... 


1st  Division 


13  Ik 

9  Chuen 

5  Ahau 
2  Oc 

8  Cib 

10  Eznab 
7  Lamat 
12  Ben 

6  Ahau  1 

65 


2d  Division 


13  Manik 
9  Cib 

6  Chicchan 
2  Men 

8  Imix 

r 

lOAkbal 

7  Ben 

12  Eznab 

6  Chicchan^ 

65 


3fl  Division 


13  Eb 

9  Imix 

5  Oc 

2  Ahau 
8  Cimi 

10  Lamat. 
7  Eznab 
12  Akbal 

6  Oc  1 

65 


-Ith  Division 

13  Caban 

9  Cimi 

6  Men 

2  Chicchan 
8  Chuen 

10  Ben 

7  Akbal 
12  Lamat 

6  Men  ' 

65 


1  The  manuscript  has  incorrectly  7. 

Applying  rule  4  (p.  253)  to  this  tonalamatl,  we  have:  4x65  ==260, 
the  exact  number  of  days  in  a  tonalamatl. 

Another  set  of  interesting  tonalamatls  is  figured  in  plate  30,  Tro- 
Cor.,  102.1  'fi^Q  £pg^  Qj^Q  ^]^ig  page  appears  in  the  second  division, 
102b,  and  is  divided  into  five  parts,  as  the  column  of  five  day  signs 
shows.  The  order  of  reading  is  from  left  to  right  in  the  pair  of 
number  columns,  as  will  appear  in  the  following  outline  of  this  tona- 
lamatl : 


1st  Division 

2d  Division 

3d  Division 

4th  Division 

5th  Division 

1st  part,  2  days,  begin- 

ning with  day  

4  Manik 

4  Cauac 

4  Chuen 

4  Akbal 

4  Men 

2d  part,  7  days,  begin- 

ning with  day  

6  Muluc 

6  Imix 

6  Ben 

6  Chicchan 

6  Caban 

3d  part,  2  days,  begin- 

ning witli  day  

13  Cib 

13  Lamat 

13  Ahau 

13  Eb 

13  Kan 

4th  part,  10  days,  begin- 

ning with  day  

2  Eznab 

2  Oc 

2  Ik 

2  Ix 

2  Cimi 

5th  part,  9  days,  begin- 

12  Lamat 

12  Ahau 

12  Eb 

12  Kan 

12  Cib 

6th  part,  22  days,  begin- 

ning with  day  

8  Caban 

8  Muluc 

8  Imix 

8  Ben 

8  Chicchan 

Total  number  of  days  

52 

52 

52 

52 

52 

264 


BUREAU  OF  AMEEICAlf  ETHNOLOGY 


[bull.  57 


Applying  rule  4  (p.  253)  to  this  tonalamatl,  we  have:  5  X 52  =  260, 
the  exact  number  of  days  in  a  tonalamatl.  The  next  tonalamatl  on 
this  page  (see  third  division  in  pi.  29,  that  is,  Tro-Cor.,  102c)  is  inter- 
esting chiefly  because  of  the  fact  that  the  pictures  which  went  with 
the  third  and  fourth  parts  of  the  five  divisions  are  omitted  for  want 
of  space.    The  outline  of  this  tonalamatl  follows: 


1st  Division 

2d  Division 

3d  Division 

4th  Division 

5th  Division 

1st  part,  17  days,  beginning 

with  day  

4  Ahau 

4Eb 

4  Kan 

4  Cib 

4  Lamat 

2d  part,  13  days,  beginning 

8  Caban 

8  Muluc 

8  Imix 

8  Ben 

8  Chicchan 

3d  part,  10  days,  beginning 

with  day  

8  Oc 

8Ik 

Six 

8  Cimi 

8  Eznab 

4th  part,  12  days,  begin- 

ning with  day  

5  Ahau 

5  £b 

5  Kan 

5  Cib 

5  Lamat 

Total  number  of  days  

52 

52 

52 

52 

52 

Applying  rule  4  (p.  253)  to  this  tonalamatl,  we  have:  5  X  52  =  260, 
the  exact  number  of  days  in  a  tonalamatl.  The  last  tonalamatl  in 
plate  29,  Tro-Cor.,  102d,  commences  with  the  same  day,  4  Ahau,  as 
the  preceding  tonalamatl  and,  like  it,  has  five  divisions,  each  of  which 
begins  with  the  same  day  as  the  corresponding  division  in  the  tona- 
lamatl just  given,  4  Ahau,  4  Eb,  4  Kan,  4  Cib,  and  4  Lamat.  Tro-Cor. 
102d  differs  from  Tro-Cor.  102c  in  the  number  and  length  of  the  parts 
into  which  its  divisions  are  divided. 

Adding  the  first  black  number,  29,  to  the  beginning  day,  4  Ahau, 
the  day  reached  will  be  7  Muluc,  of  which  only  the  7  appears  in  the 
text.  Adding  to  this  the  next  black  number,  24,  the  day  reached 
will  be  5  Ben.  An  examination  of  the  text  shows,  however,  that  the 
day  actually  recorded  is  4  Ebj  the  last  red  number  with  the  second 
day  sign.  This  latter  day  is  just  the  day  before  5  Ben,  and  since  the 
sum  of  the  black  numbers  in  this  case  does  not  equal  any  factor  of 
260  (29  +  24  =  53),  and  since  changing  the  last  black  number  from 
24  to  23  would  make  the  sum  of  the  black  numbers  equal  to  a  factor 
of  260  (29  +  23  =  52),  and  would  bring  the  count  to  4  Eb,  the  day 
actually  recorded,  we  are  justified  in  assuming  that  there  is  an  error 
in  our  original  text,  and  that  23  should  have  been  written  here  instead 
of  24.    The  outline  of  this  tonalamatl,  corrected  as  suggested,  follows : 


MofiLET]      INTRODUCTION  TO  STUDY  OP  MAYA  HIEROGLYPHS  265 


1st  Division 

2d  Division 

3d  Division 

4th  Division 

5th  Division 

1st  part,  29  days,  beginning 

with  day 

4  Ahau 

4  Eb 

4  TTaTT 

4  Cib 

d.  T.amat 

%  XiClIUCIL 

2d  part,  23  ^  days,  begin- 

ning with  day  

7  Muluc 

7  Imix 

7  Ben 

7  Chicchan 

7  Caban 

Total  number  of  days  

52 

52 

52 

52 

52 

1  The  manuscript  incorrectly  has  24. 


Applying  rule  4  (p.  253)  to  this  tonalamatl,  we  have:  52  X  5  =  200, 
the  exact  number  of  days  in  a  tonalamatl. 

The  foregoing  tonalamatls  have  been  taken  from  the  pages  of  the 
Dresden  Codex  or  those  of  the  Codex  Tro-Cortesiano.  Unfortunately, 
in  the  Codex  Peresianus  no  complete  tonalamatls  remain,  though  one 
or  two  fragmentary  ones  have  been  noted. 

No  matter  how  they  are  divided  or  with  what  days  tbey  begin,  all 
tonalamatls  seem  to  be  composed  of  the  same  essentials : 

1.  The  calendric  parts,  made  up,  as  we  have  seen  on  page  251,  of 
(a)  the  column  of  day  signs;  (h)  the  red  numbers;  (c)  the  black 
numbers. 

2.  The  pictures  of  anthropomorphic  figures  and  animals  engaged 
in  a  variety  of  pursuits,  and 

3.  The  groups  of  four  or  six  glyphs  above  each  of  the  pictures. 

The  relation  of  these  parts  to  the  tonalamatl  as  a  whole  is  practi- 
cally de.termined.  The  first  is  the  calendric  background,  the  chron- 
ological framework,  as  it  were,  of  the  period.  The  second  and  tliird 
parts  amplify  this  and  give  the  special  meaning  and  significance  to 
the  subdivisions.  The  pictures  represent  in  all  probability  the  deities 
who  presided  over  the  several  subdivisions  of  the  tonalamatls  in 
which  they  appear,  and  the  glyphs  above  them  probably  set  forth 
their  names,  as  well  as  the  ceremonies  connected  with,  or  the  prog- 
nostications for,  the  corresponding  periods. 

It  will  be  seen,  therefore,  that  in  its  larger  sense  the  meaning^  of 
the  tonalamatl  is  no  longer  a  sealed  book,  and  while  there  remains 
a  vast  amount  of  detail  yet  to  be  worked  out  the  foundation  has 
been  laid  upon  which  future  investigators  may  build  with  confidence. 

In  closing  this  discussion  of  the  tonalamatl  it  may  not  be  out  of 
place  to  mention  here  those  whose  names  stand  as  pioneers  in  this 
particular  field  of  glyphic  research.  To  the  investigations  of  Prof. 
Ernst  Forstemann  we  owe  the  elucidation  of  the  calendric  part  of 
the  tonalamatl,  and  to  Dr.  Paul  Schellhas  the  identification  of  the 
gods  and  their  corresponding  name  glyphs  in  parts  (2)  and  (3),  above. 
As  pointed  out  at  the  beginning  of  this  chapter,  the  most  promising 


266 


BUREAU  OF  AMEEICAK  ETHKOLOGY 


[bull.  57 


line  of  research  in  the  codices  is  the  groups  of  glyphs  above  the 
pictures,  and  from  their  decipherment  will  probably  come  the  deter- 
mination of  the  meaning  of  this  interesting  and  unusual  period. 

Texts  Recording  Initial  Series 

Initial  Series  in  the  codices  are  unusual  and  indeed  have  been 
found,  up  to  the  present  time,  in  only  one  of  the  three  known  Maya 
manuscripts,  namely,  the  Dresden  Codex.  As  represented  in  this 
manuscript,  they  differ  considerably  from  the  Initial  Series  heretofore 
described,  all  of  which  have  been  drawn  from  the  inscriptions.  This 
difference,  however,  is  confined  to  unessentials,  and  the  system  of 
counting  and  measuring  time  in  the  Initial  Series  from  the  inscrip- 
tions is  identical  with  that  in  the  Initial  Series  from  the  codices. 

The  most  conspicuous  difference  between  the  two  is  that  in  the 
codices  the  Initial  Series  are  expressed  by  the  second  method,  given 
on  page  129,  that  is,  numeration  by  position,  while  in  the  inscriptions, 
as  we  have  seen,  the  period  glyphs  are  used,  that  is,  the  first  method, 
on  page  105.  Although  this  causes  the  two  kinds  of  texts  to  appear 
very  dissimilar,  the  difference  is  only  superficial. 

Another  difference  the  student  will  note  is  the  absence  from  the 
codices  of  the  so-called  Initial-series  "introducing  glyph.' ^  In  a  few 
cases  there  seems  to  be  a  sign  occupying  the  position  of  the  intro- 
ducing glyph,  but  its  identification  as  the  Initial-series  "introducing 
glyph"  is  by  no  means  sure,  and,  moreover,  as  stated  above,  it  does 
not  occur  in  all  cases  in  which  there  are  Initial  Series. 

Another  difference  is  the  entire  absence  from  the  codices  of  Sup- 
plementary Series ;  this  count  seems  to  be  confined  exclusively  to  the 
monuments.  Aside  from  these  points  the  Initial  Series  from  the  two 
sources  differ  but  little.  All  proceed  from  identically  the  same  start- 
ing point,  the  date  4  Ahau  8  Cumhu,  and  all  have  their  terminal  dates 
or  related  Secondary-series  dates  recorded  immediately  after  them. 

The  first  example  of  an  Initial  Series  from  the  codices  will  be  found 
in  plate  31  (Dresden  24),  in  the  lower  left-hand  corner,  in  the  second 
column  to  the  right.  The  Initial-series  number  here  recorded  is 
9.9.16.0.0,  of  which  the  zero  in  the  2d  place  (uinals)  and  the  zero 
in  the  1st  place  (kins)  are  expressed  by  red  numbers.  This  use  of 
red  numbers  in  the  last  two  places  is  due  to  the  fact  that  the  zero 
sign  in  the  codices  is  always  red. 

The  student  will  note  the  absence  of  all  jperiod  glyphs  from  this 
Initial  Series  and  will  observe  that  the  multiplicands  of  the  cycle, 
katun,  tun,  uinal,  and  kin  are  fixed  by  the  positions  of  each  of  the 
corresponding  multipliers.  By  referring  to  Table  XIV  the  values  of 
the  several  positions  in  the  second  method  of  writing  the  numbers 
will  be  found,  and  using  these  with  their  corresponding  coefficients 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57  PLATE 


PAGE  24  OF  THE  DRESDEN  CODEX,  SHOWING 


MOELEY]      INTBODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  267 


in  each  case  the  Initial-series  number  here  recorcled  may  be  rechicod 
to  units  of  the  1st  order,  as  follows: 

9X144,000  =  1,296,000 
9  X  7,  200  =  64,  800 
16  X  360=  5,760 
OX  20  =  0 
OX  1=  0 


1,366,560 

Deducting  from  this  number  all  the  Calendar  Rounds  possible,  72 
(see  Table  XVI),  it  may  be  reduced  to  zero,  since  72  Calendar  Rounds 
contain  exactly  1,366,560  units  of  the  first  order.  See  the  preliminary 
rule  on  page  143. 

Applying  rules  1,  2,  and  3  (pp.  139,  140,  and  141)  to  the  remainder, 
that  is,  0,  the  terminal  date  of  the  Initial  Series  will  be  found  to  be 
4  Ahau  8  Cumliu,  exactly  the  same  as  the  starting  point  of  Maya 
chronology.  This  must  be  true,  since  counting  forward  0  from  the 
date  4  Ahau  8  Cumliu,  the  date  4  Ahau  8  Cumhu  will  be  reached. 
Instead  of  recording  this  date  immediately  below  the  last  period  of 
its  Initial-series  number,  that  is,  the  0  kins,  it  was  written  below  the 
number  just  to  the  left.  The  terminal  date  of  the  Initial  Series  we 
are  discussing,  therefore,  is  4  Ahau  8  Cumhu,  and  it  is  recorded  just 
to  the  left  of  its  usual  position  in  the  lower  left-hand  corner  of  plate 
31.  The  coefficient  of  the  day  sign,  4,  is  effaced  but  the  remaining 
parts  of  th'e  date  are  perfectly  clear.  Compare  the  day  sign  Ahau 
with  the  corresponding  form  in  figure  17,  c',  d' ,  and  the  month  sign 
Cumhu  with  the  corresponding  form  in  figure  20,  z-V.  The  Initial 
Series  here  recorded  is  therefore  9.9.16.0.0  4  Ahau  8  Cumhu.  Just 
to  the  right  of  this  Initial  Series  is  another,  the  number  part  of  which 
the  student  will  readily  read  as  follows:  9.9.9.16.0.  Treating  this 
in  the  usual  way,  it  may  be  reduced  thus: 

9X144,000  =  1,296,000 
9X  7,200=  64,800 
9X  360-  3,240 
16  X  20=  320 
OX  '1=  0 

1,  364,  360 

Deducting  from  this  number  all  the  Calendar  Rounds  possible,  71 
(see  Table  XVI),  it  maybe  reduced  to  16,780.  Applying  to  this 
number  rules  1,  2,  and  3  (pp.  139,  140,  and  141,  respectively),  its 
terminal  date  will  be  found  to  be  1  Ahau  18  Kayab;  this  date  is 
recorded  just  to  the  left  below  the  kin  place  of  the  'preceding  Initial 


268 


BUEEAU  OF  AMEKICAK  ETHNOLOGY 


[BULL.  57 


Series.  Compare  the  day  sign  and  month  sign  of  this  date  with 
figures  17,  c' ,  ,  and  20,  x,  y,  respectively.  This  second  Initial 
Series  in  plate  31  therefore  reads  9.9.9.16.0  1  Ahau  18  Kayab.  In 
connection  with  the  first  of  these  two  Initial  Series,  9.9.16.0.0  4  Ahau 
8  Cumliu,  there  is  recorded  a  Secondary  Series.  This  consists  of  6 
tuns,  2  uinals,  and  0  kins  (6.2.0)  and  is  recorded  just  to  the  left  of 
the  first  Initial  Series  from  which  it  is  counted,  that  is,  in  the  left- 
hand  column. 

It  was  explained  on  pages  136-137  that  the  almost  universal  direc- 
tion of  counting  was  forward,  but  that  when  the  count  was  backward 
in  the  codices,  this  fact  was  indicated  by  a  special  sign  or  symbol, 
which  gave  to  the  number  it  modified  the  significance  of  ^'backward  " 
or  ''minus."  This  sign  is  shown  in  figure  64,  and,  as  explained  on 
page  137,  it  usually  is  attached  only  to  the  lowest  period.  Keturning 
once  more  to  our  text,  in  plate  31  we  see  this  ''backward"  sign — a 
red  circle  surmounted  by  a  knot — surrounding  the  0  kins  of  this 
Secondary-series  number  6.2.0,  and  we  are  to  conclude,  therefore, 
that  this  number  is  to  be  counted  backward  from  some  date. 

Counting  it  backward  from  the  date  which  stands  nearest  it  in  our 
text,  4  Ahau  8  Cumliu,  the  date  reached  will  be  1  Ahau  18  Kayab. 
But  since  the  date  4  Ahau  8  Cumhu  is  stated  in  the  text  to  have  corre- 
sponded with  the  Initial-series  value  9.9.16.0.0,  by  deducting  6.2.0 
from  this  number  we  may  work  out  the  Initial-series  value  for  this 
date  as  follows: 

9.9.16.  0.0    4  Ahau  8  Cumliu 

6.  2.0  Backward 
9.9.  9.16.0    1  Ahau  18  Kayab 

The  accuracy  of  this  last  calculation  is  established  by  the  fact  that 
the  Initial-series  value  9.9.9.16.0  is  recorded  as  the  second  Initial 
Series  on  the  page  above  described,  and  corresponds  to  the  date  1 
Ahau  18  Kayab  as  here. 

It  is  difTicult  to  say  why  the  terminal  dates  of  these  two  Initial 
Series  and  this  Secondary  Series  should  have  been  recorded  to  the 
left  of  the  numbers  leading  to  them,  and  not  just  helow  the  numbers 
in  each  case.  The  only  explanation  the  writer  can  offer  is  that  the 
ancient  scribe  wished  to  have  the  starting  point  of  his  Secondary- 
series  number,  4  Ahau  8  Cumhu,  recorded  as  near  that  number  as 
possible,  that  is,  just  below  it,  and  consequently  the  Initial  Series 
leading  to  this  date  had  to  stand  to  the  right.  This  caused  a  dis- 
placement of  the  corresponding  terminal  date  of  his  Secondary 
Series,  1  Ahau  18  Kayab,  which  was  written  under  the  Initial  Series 
9.9.16.0.0;  and  since  the  Initial-series  value  of  1  Ahau  18  Kayab  also 
appears  to  the  right  of  9.9.16.0.0  as  9.9.9.16.0,  this  causes  a  displace- 
ment in  its  terminal  date  likewise. 


MOELBY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS 


269 


Two  other  Initial  Series  will  suffice  to  exemplify  this  kind  of  count 
in  the  codices.  In  plate  32  is  figured  page  62  from  the  Dresden 
Codex.  In  the  two  right-hand  columns  appear  two  black  numbers. 
The  first  of  these  reads  quite  clearly  8.16.15.16.1,  which  the  student 
is  perfectly  justified  in  assuming  is  an  Initial-series  number  consist- 
ing of  8  cycles,  16  katuns,  15  tuns,  16  uinals,  and  1  kin.  Moreover, 
above  the  8  cycles  is  a  glyph  which  bears  considerable  resemblance 
to  the  Initial-series  introducing  glyph  (see  fig.  24,/).  Note  in  particular 
the  trinal  superfix.  At  all  events,  whether  it  is  an  Initial  Series  or 
not,  the  first  step  in  deciphering  it  will  be  to  reduce  this  number  to 
units  of  the  first  order: 


Deducting  from  this  number  all  the  Calendar  Rounds  possible,  67 
(see  Table  XVI),  it  may  be  reduced  to  1,261.  Applying  rules  1,  2, 
and  3  (pp.  139,  140,  and  141,  respectively)  to  this  remainder,  the 
terminal  date  reached  will  be  4  Imix  9  Mol.  This  is  not  the  terminal 
date  recorded,  however,  nor  is  it  the  terminal  date  standing  below 
the  next  Initial-series  number  to  the  right,  8.16.14.15.4.  It  would 
seem  then  that  there  must  be  some  mistake  or  unusual  feature  about 
this  Initial  Series. 

Immediately  below  the  date  which  stands  under  the  Initial-scries 
number  we  are  considering,  8.16.15.16.1,  is  another  number  consisting 
of  1  tun,  4  uinals,  and  16  kins  (1.4.16).  It  is  not  improbable  that 
this  is  a  Secondary-series  number  connected  in  some  way  with  our 
Initial  Series.  The  red  circle  surmounted  by  a  knot  which  surrounds 
the  16  kins  of  this  Secondary-series  number  (1.4.16)  indicates  that 
the  whole  number  is  to  be  counted  hacJcward  from  some  date.  Ordi- 
narily, the  first  Secondary  Series  in  a  text  is  to  be  counted  from  the 
terminal  date  of  the  Initial  Series,  which  we  have  found  by  calcula- 
tion (if  not  by  record)  to  be  4  Imix  9  Mol  in  this  case.  Assuming 
that  this  is  the  case  here,  we  might  count  1.4.16  hacJcward  from  the 
date  4  Imix  9  Mol. 

Performing  all  the  operations  indicated  in  such  cases,  the  terminal 
date  reached  will  be  foimd  to  be  3  Chicclian  18  Zip ;  this  is  very  close 
to  the  date  which  is  actually  recorded  just  above  the  Secondary- 
series  number  and  just  below  the  Initial-series  number.  The  date 
here  recorded  is  3  Chiccliaii  13  Zip,  and  it  is  not  improbable  that  the 


8  X 144,  000 
16  X  7,  200 
15 X  360 
16  X  20 

IX  0 


1,  152,  000 
115,  200 
5,  400 
320 
1 


1,  272,  921 


270 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


ancient  scribe  intended  to  write  instead  3  Chicchan  18  Zip,  the  date 
indicated  bj  the  calculations.    We  probably  have  here: 

8.16.15.16.  1    (4  Imix  9  Mol) 

1.  4.16  Backward 
8.16.14.11.  5     3  Chicchan  18  ^  Zip 

In  these  calculations  the  terminal  date  of  the  Initial  Series,  4  Imix 
9  Mol,  is  suppressed,  and  the  only  date  given  is  3  Chicclian  18  Zip, 
the  terminal  date  of  the  Secondary  Series. 

Another  Initial  Series  of  this  same  kind,  one  in  which  the  terminal 
date  is  not  recorded,  is  shown  just  to  the  right  of  the  preceding  in 
plate  32.  The  Initial-series  number  8.16.14.15.4  there  recorded 
reduces  to  units  of  the  first  order  as  follows : 

8X144,000  =  1,  152,  000 
16  X    7,200=  115,200 

14  X        360=  5,040 

15  X         20=  300 
4X  1=  4 


1,  272,  544 


Deducting  from  this  number  all  the  Calendar  Rounds  possible,  67 
(see  Table  XVI),  it  will  be  reduced  to  884,  and  applying  rules  1,  2, 
and  3  (pp.  139,  140,  and  141,  respectively)  to  this  remainder,  the 
terminal  date  reached  will  be  4  Kan  17  Yaxkin.  This  date  is  not 
recorded.  There  follows  below,  however,  a  Secondary-series  number 
consisting  of  6  uinals  and  1  kin  (6.1).  The  red  circle  around  the 
lower  term  of  this  (the  1  kin)  indicates  that  the  whole  number,  6.1, 
is  to  be  counted  lackward  from  some  date,  probably,  as  in  the  pre- 
ceding case,  from  the  terminal  date  of  the  Initial  Series  above  it. 
Assuming  that  this  is  the  case,  and  counting  6.1  backward  from 
8.16.14.15.4  4  Kan  17  Yaxkin,  the  terminal  date  reached  will  be  13 
Akbal  16  Pop,  again  very  close  to  the  date  recorded  immediately 
above,  13  Akbal  16  Pop.  Indeed,  the  date  as  recorded,  13  Akbal 
16  Pop,  represents  an  impossible  condition  from  the  Maya  point  of 
view,  since  the  day  name  Akbal  could  occupy  only  the  first,  sixth, 
eleventh,  and  sixteenth  positions  of  a  month.  See  Table  VII.  Con- 
sequently, through  lack  of  space  or  carelessness  the  ancient  scribe 
who  painted  this  book  failed  to  add  one  dot  to  the  three  bars  of  the 
month  sign's  coefficient,  thus  making  it  16  instead  of  the  15  actually 
recorded.  We  are  obliged  to  make  some  correction  in  this  coefficient, 
since,  as  explained  above,  it  is  obviously  incorrect  as  it  stands. 
Since  the  addition  of  a  single  dot  brings  the  whole  date  into  harmony 
with  the  date  determined  by  calculation,  we  are  probably  justified 

1  Incorrectly  recorded  as  13  in  the  text- 


MORLEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  271 


in  making  the  correction  here  suggested.  We  have  recorded  here 
therefore : 

8.16.14.15.4    (4  Kan  17  Yaxkin) 

6.1  Backward 
8.16.14.  9.3    13  Akbal  16  ^  Pop 

In  these  calculations  the  terminal  date  of  the  Initial  Series,  4  Kan 
17  Yaxkin,  is  suppressed  and  the  only  date  given  is  13  Akbal  16  Pop, 
the  terminal  date  of  the  Secondary  Series. 

The  above  will  suffice  to  show  the  use  of  Initial  Series  in  the 
codices,  but  before  leaving  this  subject  it  seems  best  to  discuss 
briefly  the  dates  recorded  by  these  Initial  Series  in  relation  to  the 
Initial  Series  on  the  monuments.  According  to  Professor  Forste- 
mann^  there  are  27  of  these  altogether,  distributed  as  follows: 


Page  24 

:     9.  9.16.  0. 

0^ 

Page  58 

.  9.12.11.11. 

0 

Page  24 

:     9.  9.  9.16. 

0 

Page  62 

8.16.15.16. 

1 

Page  31 

:  8.16.14.15. 

4 

Page  62 

8.16.74.15. 

4 

Page  31 

8.16.  3.13. 

0 

Page  63 

8.11.  8.  7. 

0 

Page  31 

10.13.13.  3. 

2  * 

Page  63 

8.16.  3.13. 

0 

Page  43 

9.19.  8.15. 

0 

Page  63 

10.13.  3.16. 

49 

Page  45 

8.17.11.  3. 

0 

Page  63 

10.13.13.  3. 

2 

Page  51 

8.16.  4.  8. 

0^ 

Page  70 

9.13.12.10. 

0 

Page  51 

10.19.  6.  1. 

8« 

Page  70 

9.19.11.13. 

0 

Page  52 

9.16.  4.11.18^ 

Page  70 

10.17.13.12.12 

Page  52 

9.19.  5.  7. 

8« 

Page  70 

10.11.  3.18.14 

Page  52 

9.16.  4.10. 

8 

Page  70 

8.  6.16.12. 

0 

Page  52 

9.16.  4.11. 

3 

Page  70 

8.16.19.10. 

0 

Page  58 

9.18.  2.  2. 

0 

There  is  a  wide  range  of  time  covered  by  these  Initial  Series;  indeed, 
from  the  earliest  8.6.16.12.0  (on  p.  70)  to  the  latest,  10.19.6.1.8  (on 
p.  51)  there  elapsed  more  than  a  thousand  years.  Where  the  differ- 
ence between  the  earliest  and  the  latest  dates  is  so  great,  it  is  a  matter 
of  vital  importance  to  determine  the  contemporaneous  date  of  the 
manuscript.  If  the  closing  date  10.19.6.1.8  represents  the  time  at 
which  the  manuscript  was  made,  then  the  preceding  dates  reac'h  back 

1  Incorrectly  recorded  as  15  ia  the  text. 

2  Bull.  28,  Bur.  Amer.  Ethn.,  p.  400. 

3  The  terminal  dates  reached  have  been  omitted,  since  for  comparative  work  the  Initial-scries  num- 
bers alone  are  sufficient  to  show  the  relative  positions  in  the  Long  Count. 

<  The  manuscript  incorrectly  reads  10.13.3.13.2;  that  is,  reversing  the  position  of  the  tun  and  uinal  coeffi- 
cients. 

5  The  manuscript  incorrectly  reads  8.16.4.11.0.   The  uinal  coefficient  is  changed  to  an  8,  above. 

6  The  manuscript  incorrectly  reads  10.19.6.0.8.   The  uinal  coefficient  is  changed  to  1,  above. 

7  The  manuscript  incorrectly  reads  9.16.4.10.18.   The  uinal  coefficient  is  changed  to  11,  above. 

8  The  manuscript  incorrectly  reads  9.19.8.7.8.   The  tun  coefficient  is  changed  to  5,  above. 

9  The  manuscript  incorrectly  reads  10.8.3.16.4.  The  katun  coefficient  is  changed  to  13,  above.  These 
corrections  are  all  suggested  by  Professor  Forstemann  and  are  necessary  if  the  calculations  he  suggests  are 
correct,  as  seems  probable. 


272 


BTJKEAU  OF  AMEEICAl^  ETHNOLOGY 


[bull.  57 


for  more  than  a  thousand  years.  On  the  other  hand,  if  8.6.16.12.0 
records  the  present  time  of  the  manuscript,  then  all  the  following 
dates  are  prophetic.  It  is  a  difficult  question  to  answer,  and  the 
best  authorities  have  seemed  disposed  to  take  a  middle  course, 
assigning  as  the  coAtemporaneous  date  of  the  codex  a  date  about  the 
middle  of  Cycle  9.  Says  Professor  Forstemann  {Bulletin  28,  p.  402) 
on  the  subject: 

In  my  opinion  my  demonstration  also  definitely  proves  that  these  large  numbers 
[the  Initial  Series]  do  not  proceed  from  the  future  to  the  past,  but  from  the  past, 
through  the  present,  to  the  future.  Unless  I  am  quite  mistaken,  the  highest  numbers 
among  them  seem  actually  to  reach  into  the  future,  and  thus  to  have  a  prophetic 
meaning.  Here  the  question  arises.  At  what  point  in  this  series  of  numbers  does  the 
present  lie?  or,  Has  the  writer  in  different  portions  of  his  work  adopted  different 
points  of  time  as  the  present?  If  I  may  venture  to  express  my  conjecture,  it  seems 
to  me  that  the  first  large  number  in  the  whole  manuscript,  the  1,366,560  in  the  second 
column  of  page  24  [9.9.16.0.0  4  Ahau  8  Cumhu,  the  first  Initial  Series  figured  in  plate 
31],  has  the  greatest  claim  to  be  interpreted  as  the  present  point  of  time. 

In  a  later  article  {Bulletin  28,  p.  437)  Professor  Forstemann  says: 
''But  I  think  it  is  more  probable  that  the  date  farthest  to  the  right 
(1  Ahau,  18  Zip  .  .  .  )  denotes  the  present,  the  other  two 
[namely,  9.9.16.0.0  4  Ahau  8  Cumliu  and  9.9.9.16.0  1  Ahau  18  Kayab] 
alluding  to  remarkable  days  in  the  future."  He  assigns  to  this  date 
1  Ahau  18  Zip  the  position  of  9.7.16.12.0  in  the  Long  Count. 

The  writer  believes  this  theory  to  be  untenable  because  it  involves 
a  correction  in  the  original  text.  The  date  which  Professor  Forste- 
mann calls  1  Ahau  18  Zip  actually  reads  1  Ahau  18  Uo,  as  he  himself 
admits.  The  month  sign  he  corrects  to  Zip  in  spite  of  the  fact  that 
it  is  very  clearly  Uo.  Compare  this  form  with  figure  20,  h,  c.  The 
date  1  Ahau  18  Uo  occurs  at  9.8.16.16.0,  but  the  writer  sees  no  reason 
for  believing  that  this  date  or  the  reading  suggested  by  Professor 
Forstemann  indicates  the  contemporaneous  time  of  this  manuscript. 

Mr.  Bowditch  assigns  the  manuscript  to  approximately  the  same 
period,  selecting  the  second  Initial  Series  in  plate  31,  that  is, 
9.9.9.16.0  1  Ahau  18  Kayab:  ''My  opinion  is  that  the  date  9.9.9.16.0 
1  Ahau  18  Kayab  is  the  present  time  with  reference  to  the  time  of 
writing  the  codex  and  is  the  date  from  which  the  whole  calculation 
starts."^  The  reasons  which  have  led  Mr.  Bowditch  to  this  conclu- 
sion are  very  convincing  and  will  make  for  the  general  acceptance  of 
his  hypothesis. 

Although  the  writer  has  no  better  suggestion  to  offer  at  the  present 
time,  he  is  inclined  to  believe  that  both  of  these  dates  are  far  too 
early  for  this  manuscript  and  that  it  is  to  be  ascribed  to  a  very  much 
later  period,  perhaps  to  the  centuries  following  immediately  the  colo- 
nization of  Yucatan.  .  There  can  be  no  doubt  that  very  early  dates 
appear  in  the  Dresden  Codex,  but  rather  than  accept  one  so  early  as 

1  Bowditch,  1909:  p.  279. 


BUREAU  OF  AMERICAN  ETHNOLOGY 


BULLETIN  57    PLATE  32 


PAGE  62  OF  THE  DRESDEN  CODEX,  SHOWING  THE 
SERPENT  NUMBERS 


MOELEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEEOGLYPilS  275 


are  discussing  sheds  no  light  on  this  question.    There  are,  liowevcr, 
two  other  pages  in  this  Codex  (61  and  69)  on  which  Serpent  numhers 
appear  presenting  this  date,  9  Kan  12  Kayab,  under  conchtions  wliich 
may  shed  light  on  the  position  it  held  in  the  Long  Count.    On  page 
69  there  are  recorded  15  katuns,  9  tuns,  4  uinals,  and  4  kins  (s(h^  fig. 
85);  these  are  immediately  followed  by  the  date  9  Kan  12  Kayab. 
It  is  important  to  note  in  this  connection  that,  unlike  almost  every 
other  number  in  this  codex,  this  number  is  expressed  by  the  first 
method,  the  one  in  which  the  period  glyphs  are  used.    As  the  date 
4  Ahau  8  Cumhu  appears  just  above  in  the  text,  the  first  supposition 
is  that  15.9.4.4  is  a  Secondary-series  number  which,  if  counted  for- 
ward from  4  Aliau  8  Cumhu,  the  starting  point  of  Maya  chronology, 
will  reach  9  Kan  12  Kayab,  the  date  recorded  immediately  after  it. 
Proceeding  on  this  assumption  and  performing  the  — —  •••m. 
operations  indicated,  the  terminal  date  reached  will  ^^^^ 
be  9  Kan  7  Cumbu,  not  9  Kan  12  Kayab,  as  recorded. 
The  most  plausible  explanation  for  this  number  and  jOT 
date  the  writer  can  offer  is  that  the  whole  constitutes    •^B  •f^o 
a  Period-ending  date.    On  the  west  side  of  Stela  C  at  *J^L*j|(J^ 
Quirigua,  as  explained   on   page   226,  is    a  Period-  vLnii'*!!®© 
ending  date  almost  exactly  like  this  (see  pi.  21,  H).   fig.  85.  Exam- 
On  this  monument  17:5.0.0  6  Ahau  13  Kayab  is  record-  P^^^^f 

method  of  nu- 

ed,  and  it  was  proved  by  calculation  that  9.17.5.0.0  mcration  in  the 
would  lead  to  this  date  if  counted  forward  from  the     ^"^i^^^  (part  of 

page  09  of  the 

starting  point  of  Maya  chronology.    In  effect,  then,     Dresden  Co- 
this  17.5.0.0  6  Ahau  13  Kayab  was  a  Period-ending 
date,  declaring  that  Tun  5  of  Katun  17  (of  Cycle  9,  unexpressed) 
ended  on  the  date  6  Abau  13  Kayab. 

Interpreting  in  the  same  way  the  glyphs  in  figure  85,  we  have  the 
record  that  Kin  4  of  Uinal  4  of  Tun  9  of  Katun  15  (of  Cycle  9,  unex- 
pressed) fell  (or  ended)  on  the  date  9  Kan  12  Kayab.  Changing  this 
Period-ending  date  into  its  corresponding  Initial  Series  and  solving 
for  its  terminal  date,  the  latter  date  will  be  found  to  be  13  Kan  12  Ceh, 
instead  of  9  Kan  12  Kayab.  At  first  this  would  appear  to  be  even  farther 
from  the  mark  than  our  preceding  attempt,  but  if  the  reader  will  admit 
a  slight  correction,  the  above  number  can  be  made  to  reach  the  date 
recorded.  The  date  13  Kan  12  Ceh  is  just  5  uinals  earlier  than  9  Kan 
12  Kayab,  and  if  we  add  one  bar  to  the  four  dots  of  the  uinal  coeffi- 
cient, this  passage  can  be  explained  in  the  above  manner,  and  yet 
agree  in  all  particulars.  This  is  true  since  9.15.9.9.4  reaches  the  date 
9  Kan  12  Kayab.  On  the  above  grounds  the  writer  is  inclined  to 
believe  that  the  last  three  Serpent  numbers  on  plate  32,  which  were 
shown  to  have  proceeded  from  a  date  9  Kan  12  Kayab,  were  counted 
from  the  date  9.15.9.9.4  9  Kan  12  Kayab. 


276 


BUKEAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


Texts  Eecording  Ascending  Series 

There  remains  one  other  class  of  numbers  which  should  be  described 
before  closing  this  chapter  on  the  codices.  The  writer  refers  to  the 
series  of  related  numbers  which  cover  so  many  pages  of  the  Dresden 
Codex.  These  commence  at  the  bottom  of  the  page  and  increase 
toward  the  top,  every  other  number  in  the  series  being  a  multiple  of 
the  first,  or  beginning  number.  One  example  of  this  class  will 
suffice  to  illustrate  all  the  others. 

In  the  lower  right-hand  corner  of  plate  31  a  series  of  this  kind 
commences  with  the  day  9  Ahau.^  Of  this  series  the  number  8.2.0 
just  above  the  9  Ahau  is  the  first  term,  and  the  day  9  Ahau  the  first 
terminal  date.  As  usual  in  Maya  texts,  the  starting  point  is  not 
expressed ;  by  calculation,  however,  it  can  be  shown  to  be  1  Ahau  ^ 
in  this  particular  case. 

Counting  forward  then  8.2.0  from  1  Ahau,  the  unexpressed  starting 
point,  the  first  terminal  date,  9  Ahau,  will  be  reached.  See  the  lower 
right-hand  corner  in  the  following  outhne,  in  which  the  Maya  num- 
bers have  all  been  reduced  to  units  of  the  first  order : 


151,840  ' 

113,880  3 

75,920  ^ 

37,960 ' 

1  Ahau 

1  Ahau 

1  Ahau 

1  Ahau 

185,120 

68,900 

33,280 

9,100 

1  Ahau 

1  Ahau 

1  Ahau 

1  Ahau 

35,040 

32,120 

29,200 

26,280 

6  Ahau 

11  Ahau 

3  Ahau 

8  Ahau 

23,360 

20,440 

17,520 

14,600 

13  Ahau 

5  Ahau 

10  Ahau 

2  Ahau 

11,680  ^ 

8,760 

5,840 

2,920 

7  Ahau 

12  Ahau 

4  Ahau 

9  Ahau 

(Unex 

pressed  starting  point,  1  Ahau.) 

In  the  above  outline  each  number  represents  the  total  distance  of 
the  day  just  below  it  from  the  unexpressed  starting  point,  1  Ahau,  not 
the  dis-tance  from  the  date  immediately  preceding  it  in  the  series. 
For  example,  the  second  number,  5,840  (16.4.0),  is  not  to  be  counted 
forward  from  9  Ahau  in  order  to  reach  its  terminal  date,  4  Ahau,  but 
from  the  unexpressed  starting  point  of  the  whole  series,  the  day  1 
Ahau.  Similarly  the  third  number,  8,760  (1.4.6.0),  is  not  to  be 
counted  forward  from  4  Ahau  in  order  to  reach  12  Ahau,  but  from 
1  Ahau  instead,  and  so  on  throughout  the  series. 

1  In  the  text  the  coefficient  appears  to  be  8,  but  in  reality  it  is  9,  the  lower  dot  having  been  covered  by 
the  marginal  line  at  the  bottom. 

2  Cotmting  backward  8.2.0  (2,920)  from  9  Ahau,  1  Ahau  is  reached. 

3  Professor  Forstemann  restored  the  top  terms  of  the  four  numbers  in  this  row,  so  as  to  make  them  read 
as  given  above. 

i  The  manuscript  reads  1.12.5.0,  which  Professor  Forstemann  corrects  to  1.12.8.0;  in  other  words,  chang- 
ing the  uinal  from  5  to  8.   This  correction  is  fully  justified  in  the  above  calculations. 


MOELEY]      INTRODUCTION  TO  STUDY  OF  MAYA  HIEROGLYPHS  277 


Beginning  with  the  number  2,920  and  the  starting  point  1  Ahau, 
the  first  twelve  terms,  that  is,  the  numbers  in  the  three  lowest  rows, 
are  the  first  12  multiples  of  2,920. 


The  days  recorded  under  each  of  these  numbers,  as  mentioned  above, 
are  the  terminal  dates  of  these  distances  from  the  starting  point, 
1  Ahau.  Passing  over  the  fourth  row  from  the  bottom,  which,  as 
will  appear  presently,  is  probably  an  interpolation  of  some  kind,  the 
thirteenth  number — that  is,  the  right-hand  one  in  the  top  row — is 
37,960.  But  37,960  is  13x2,920,  a  continuation  of  our  series  the 
twelfth  term  of  which  appeared  in  the  left-hand  number  of  the  third 
row.  Under  the  thirteenth  number  is  set  down  the  day  1  Ahau ;  in 
other  words,  not  until  the  thirteenth  multiple  of  2,920  is  reached  is 
the  terminal  day  the  same  as  the  starting  point. 

With  this  thirteenth  term  2,920  ceases  to  be  the  unit  of  increase,  and 
the  thirteeth  term  itself  (37,960)  is  used  as  a  difference  to  reach  the 
remaining  three  terms  on  this  top  line,  all  of  which  are  multiples  of 


Counting  forward  each  one  of  these  from  the  starting  point  of  this 
entire  series,  1  Ahau,  each  will  be  found  to  reach  as  its  terminal  day 
1  Ahau,  as  recorded  under  each.  The  fourth  line  from  the  bottom  is 
more  difficult  to  understand,  and  the  explanation  offered  by  Professor 
Forstemann,  that  the  first  and  third  terms  and  the  second  and  fourth 
are  to  be  combined  by  addition  or  subtraction,  leaves  much  to  be 
desired.  Omitting  this  row,  however,  the  remaining  numbers,  those 
which  are  multiples  of  2,920,  admit  of  an  easy  explanation. 

In  the  first  place,  the  opening  term  2,920,  which  serves  as  the  unit 
of  increase  for  the  entire  series  up  to  and  including  the  13th  term,  is 
the  so-called  Venus-Solar  period,  containing  8  Solar  years  of  365 
days  each  and  5  Venus  years  of  584  days  each.  This  important 
period  is  the  subject  of  extended  treatment  elsewhere  in  ihe  Dresden 
Codex  (pp.  46-50),  in  which  it  is  repeated  39  times  in  all,  divided 
into  three  equal  divisions  of  13  periods  each.  The  13th  term  of  our 
series  37,960  is,  as  we  have  seen,  13x2,920,  the  exact  number  of 


2,920 
5,840 
8,760 
11,680 
14,600 
17,520 


1X2,920 
2X2,920 
3X2,920 
4X2,920 
5X2,920 
6X2,920 


20,440=  7X2,920 
23,360=  8X2,920 
26,280=  9X2,920 
29,200  =  10X2,920 
32,120  =  11  X2,920 
35,040  =  12X2,920 


37,960. 


37,960  =  1  X  37,960  or  13  X  2,920 
75,920  =  2  X  37,960  or  26  X  2,920 
113,880  =  3X37,960  or  39x2,920 
151,840  =  4X37,960  or  52x2,920 


278 


BUREAU  OF  AMERICAN  ETHNOLOGY 


[bull.  57 


days  treated  of  in  the  upper  divisions  of  pages  46-50  of  the  Dresden 
Codex.  The  14th  term  (75,920)  is  the  exact  number  of  days  treated 
of  in  the  first  two  divisions,  and  finally,  the  15th,  or  next  to  the  last 
term  (113,880),  is  the  exact  number  of  days  treated  of  in  all  three 
divisions  of  these  pages. 

This  13th  term  (37,960)  is  the  first  in  which  the  tonalamatl  of  260 
days  comes  into  harmony  with  the  Venus  and  Solar  years,  and  as 
such  must  have  been  of  very  great  importance  to  the  Maya.  At  the 
same  time  it  represents  two  Calendar  Rounds,  another  important 
chronological  count.  With  the  next  to  the  last  term  (113,880)  the 
Mars  year  of  780  days  is  brought  into  harmony  with  all  the  other 
periods  named.  This  number,  as  just  mentioned,  represents  the  sum 
of  all  the  39  Venus-Solar  periods  on  pages  46-50  of  the  Dresden 
Codex.  This  next  to  the  last  number  seems  to  possess  more  remark- 
able properties  than  the  last  number  (151,840),  in  which  the  Mars 
year  is  not  contained  without  a  remainder,  and  the  reason  for  its 
record  does  not  appear. 

The  next  to  the  last  term  contains : 

438  Tonalamatls  of  260  days  each 
312  Solar  years  of  365  days  each 
195  Venus  years  of  584  days  each 
146  Mars  years  of  780  days  each 
39  Venus-Solar  periods  of  2,920  days  each 
6  Calendar  Rounds  of  18,980  days  each 

It  will  be  noted  in  plate  31  that  the  concealed  starting  point  of  this 
series  is  the  day  1  Ahau,  and  that  just  to  the  left  on  the  same  plate 
are  two  dates,  1  Ahau  18  Kayab  and  1  Ahau  18  Uo,  both  of  which  show 
this  same  day,  and  one  of  which,  1  Ahau  18  Kayab,  is  accompanied 
by  its  corresponding  Initial  Series  9.9.9.16.0.  It  seems  not  unHkely, 
therefore,  that  the  day  1  Ahau  with  which  this  series  commences  was 
1  Ahau  18  Kayab,  which  in  turn  was  9.9.9.16.0  1  Ahau  18  Kayab  of 
the  Long  Count.  This  is  rendered  somewhat  probable  by  the  fact 
that  the  second  division  of  13  Venus-Solar  periods  on  pages  46-50 
of  the  Dresden  Codex  also  has  the  same  date,  1  Ahau  18  Kayab,  as 
its  terminal  date.  Hence,  it  is  not  improbable  (more  it  would  be  un- 
wise to  say)  that  the  series  of  numbers  which  we  have  been  dis- 
cussing was  counted  from  the  date  9.9.9.16.0.  1  Ahau  18  Kayab. 

The  foregoing  examples  cover,  in  a  general  way,  the  material 
presented  in  the  codices;  there  is,  however,  much  other  matter  which 
has  not  been  explained  here,  as  unfitted  to  the  needs  of  the  beginner. 
To  the  student  who  wishes  to  speciaUze  in  this  field  of  the  glyphic 
writing  the  writer  recommends  the  treatises  of  Prof.  Ernst  Forste- 
mann  as  the  most  valuable  contribution  to  this  subject. 


INDEX 


Page 

Abbeeviation  m  dating,  use   222, 252 

Addition,  metliod   149 

Adultery,  punishment   9-10 

Agtjilar,  S.  de,  on  Maya  records   36 

Ahholpop  (official),  duties   13 

Ahktjlel  (deputy-chief),  powers   13 

Ahptjch  (god),  nature   17 

Alphabet,  nonexistence   27 

Amusements,  nature   10 

Arabic  system  of  numbers,  Maya  parallel . .  87, 96 

Architecture,  development   5 

Arithmetic,  system   87-155 

Ascending  series,  texts  recording   276-278 

Astronomical  computations— 

accuracy   32 

in  codices   31-32,276-278 

Aztec— 

calendar   58-59 

ikomomatic  hieroglyphics   29 

rulership  succession   16 

Backward  sign— 

glyph   137 

use   137,268 

Bakhalal  (city),  founding   4 

Bar,  numerical  value   87-88 

Bar  and  dot  numerals— 

antiquity  -   102-103 

examples,  plates  showing   157, 

167, 170, 176, 178, 179 

form  and  nature   87-95 

Batab  (chief),  powers   13 

Bibliography   xv-xvi 

BOWDITCH,  C.  P — 

cited   2,45,65,117,134,203 

on  dating  system   82-83, 214-215, 272 

on  hieroglyphics   30, 33, 71 

on  Supplementary  Series   152 

works  -  vii-viii 

Brinton,  Dr.  D.  G — 

error  by   82 

on  hieroglyphics   3,23,27-28,30,33 

on  numerical  system   91 

Calendar — 

harmonization   44,215 

starting  point   41-43, 60-62, 113-114 

subdivisions   37-86 

See  also  Calendar  Round;  Chronology; 
Dating;  Long  Count. 

Calendar  Round— 

explanation  -   51-59 

glyph...   ^9 


Pago 

Calendar-round  dating— 

examples   '210-215 

limitations   7() 

Chakanputan  (city),  founding  and  destruc- 
tion  4 

Chichen  Itza  (city)— 

•      history...   3,4,5,202-203 

Temple  of  the  Initial  Series,  lintel,  inter- 
pretation  199 

Chilan  balam — 

books  of   3 

chronology  based  on   2 

Chronology— 

basis   58 

correlation   2 

duration   222 

starting  point. . .  60-62, 113-114, 124-125, 147-148 
See  alao  Calendar. 
Cities,  southern— 

occupancy  of,  diagram  showing   15 

rise  and  fall  of   2-5 

Civilization,  rise  and  fall   1-7 

Closing   sign    of    Supplementary  Series, 

glyph  -  -  152-1.53,170 

Closing  signs.  See  Ending  signs. 

Clothing,  character   7-8 

CocoM  f.vmily,  tyranny   5-6, 12 

Codex  Peresianus,  tonalamatls  named  in. .  205 

Codex  Tro-Cortesianus,  texts   262-265 

Codices— 

astronomical  character   31-32,276-278 

character  in  general   31,252 

colored  glyphs  used  in   91,251 

dates  of   203 

day  signs  in   39 

errors   270-271,274 

examples  from,  interpretation   251-278 

glyphs  for  twenty  (20)  used  in  92, 130 

historical  nature   32-33, 35-36 

Initial-series  dating  in   266 

examples   206-273 

interpretation   31-33, 254-278 

numeration  glyphs  used  in. . . .  103-104, 129-134 

order  of  reading  22, 133, 135, 137, 252-253 

tonalamatls  in   251-266 

zero  glyph  used  in   94 

Coefficients,  numerical.  See  Numerical 
coefficients. 

COGOLLUDO,  C.  L.,  on  dating  system   34,84 

Colored  glyphs,  use  of,  in  codices  91,251 

Commerce,  customs   9 

Computation,  possibility  of  errors  in   154-155 

Confederation,  formation  and  disruption. .  4-5 

279 


280 


INDEX 


COPAN  (city)—  Page 

Altar  Q.  error  on   246,248 

Altar  S,  interpretation   231-233 

Altar  Z ,  interpretation   242 

history   15 

Stela  A,  interpretation   169-170 

Stela  B,  interpretation   167-169 

Stela  D,  interpretation   188-191 

Stela  J,  interpretation   191-192 

Stela  M,  interpretation   175-176 

Stela  N,  error  on   248-249 

interpretation   114-118,248-249 

Stela  P,  interpretation   185 

Stela  2,  interpretation   223 

Stela  4,  interpretation   224-225 

Stela  6,  interpretation   170-171 

Stela  8,  interpretation   229 

S  tela  9,  antiquity   173 

interpretation   171-173 

Stela  15,  interpretation   187-188 

Cresson,  H.  T.,  cited   27 

Customs.  See  Manners  and  customs. 

Cycle— 

glyphs   68 

length  62,135 

number  of,  in  great  cycle   107-114 

numbering  of,  in  inscriptions   108, 227-233 

Cycle  8,  dates   194-198,228-220 

Cycle  y— 

dates   172,183,185,187,194,222 

prevalence  in  Maya  dating   194 

Cycle  10,  dates   199-203,229-233 

Cycle,  Great— 

length  -   135,162 

number  of  cycles  in   107-114 

Cycles,  Great,  Great,  and  Higher— 

discussion   114-129 

glyphs   118 

omitted  in  dating   126 


Dates— 

abbreviation   222,252 

errors  in  computing   154-155 

errors  in  originals   245-250, 270-271, 274 

interpretation,  in  Initial  Series.  157-222, 233-245 

in  Period  Endings   222-245 

in  Secondary  Series   207-222, 233-245 

monuments  erected  to  mark —  33-35,  249-250 

of  same  name,  distinction  between   147-151 

repetition   147 

shown  by  red  glyphs  in  codices   251 

Dates,  Initial.  See  Initial-series  dating. 

Dates  Initial  and  Secondary,  interpreta- 
tion  207-222 

Dates,  Initial,  Secondary,  and  Period- 
ending,  interpretation   233-245 

Dates,  Period-ending.  See  Period-ending 
dates. 

Dates,  Prophetic— 

examples   229-233 

use   271-272 

Dates,  Secondary.  See  Secondary-series 
dating. 

Dates,  Terminal— 

absence   218 

finding   138-154 

importance   154-155 

position   151-154 


Dating —  Page 

.  methods   46-47,63-86 

change   4 

See  also  Calendar-round  dating; 
Initial-series;  Period-ending; 
Secondary-series. 

starting  point   60-62, 113-114, 124-125 

determination   135-136 

Day— 

first  of  year   52-53 

glyphs   38,39,72,76 

coefficients   41-43,47-48 

position   127-128 

omission   127-128,208 

identification   41-43,46-48 

names   37-41,112 

numbers   111-112 

position  in  solar  year   52-58 

round  of   42-44 

Days,  Intercalary,  lack  of   45 

Days,  unlucky,  dates   45-46 

Death,  fear  of  -   11, 17 

Death  God— 

glyph   17,257 

nature   17 

Decimal  system,  parallel   129 

See  also  Vigesimal  system. 
Destruction  of  the  World,  description ...  32 

DmNATiON,  codices  used  for   31 

Dn'ORCE,  practice   9 

Dot,  numerical  value   87-88 

Dot  and  BAR  NUMBERS.  See  Bar  and  dot 

NUMBERS. 

Dresden  codex— 

date   271-273 

publication   iii 

texts   254-262,266-278 

plates  showing   32, 254, 260, 266, 273 

DRUNKENNESS,  prevlaence   10 

Ek  Ahau  (god),  nature   17-18 

ENDENTG  SIGNS— 

in  Period-ending  dates   102 

in  "zero"   101-102 

Enumeration— 

systems   87-134 

comparison  '.   133 

See  also  Numerals. 

Errors  in  texts— 

examples   245-250,270-271,274 

plate  showing   248 

Feathered  Serpent  (god),  nature   16-17 

Feber-paper  BOOKS.  See  Codices. 

Fish,  used  in  introducing  glyph   65-66, 188 

FivE-TUN  period.  See  Hotun. 

FORSTEMANN,  Prof.  ERNST— 

cited  ■  --  26,137 

investigations   iii,  265, 276 

methods  of  solving  numerals   134 

on  hieroglyphics   30 

on  prophetic  dates   272 

FUXI--FIGURE  glyphs— 

nature   67-68,18^191 

plate  showing   188 

See  also  Time  periods. 

Funeral  CUSTOMS,  description   11-12 

FUTURE  LIFE,  belief  as  to   19 


INDEX 


Page 

Glyph  block,  definition   156 

Glyphs.  See  Hieroglyphs. 

Gods,  nature   16-19 

Goodman,  J,  T.— 

chronologic  tables  of   134 

cited  2,44,116-117,123 

investigation  iii-iv 

on  introducing  glyph   66 

on  length  of  great  cycle   108 

on  Supplementary  Series   152 

Government,  nature   12-16 

Great  Cycle— 

length   135 

number  of  cycles  in   107-114 

Haab  (solar  year)— 

first  day  52-56 

glyph   47 

nature   44-51 

position  of  days  in   48,52-58 

subdivisions  ,   45 

Habitat  of  the  Maya   1-2 

map   1 

Hair,  method  of  dressing   7 

Halach  UiNic  (chief),  powers   12-13 

Hand,  used  as  ending  sign   101-102 

Head-variant  numerals— 

pntiquity   73,102-103 

characteristics   97-103 

derivation   74 

discovery   iii 

explanation   24-25, 87, 96-104 

forms   96-104 

value   103 

identification  96-103 

parallel  to  Arabic  numerals   87 

plates  showing   167,170,176,178,179,180 

use  of,  in  time-period  glyphs   67-74, 104 

See  aZso t'ULL-FiGURE  glyphs. 

Hewett,  Dt.  E.  L.,  cited   164, 192 

Hieroglyphs— 

antiquity   iii,  2 

proofs   173,175 

character   iv,  26-30 

classification   26 

decipherment   23-25, 31, 249-250 

errors  in  interpretation   154-155 

errors  in  original  text   245-250 

methods   134-155 

inversion  of  significance   211 

mat  pattern   191-194 

materials  inscribed  upon   22 

modifications  23-25 

order  of  reading   23, 

129, 133, 135, 136-138, 156, 170, 268 

original  errors   245-250 

progress   iv,250 

symmetry   23-24,88-91,128 

textbooks   vii 

See  also  Numerals. 

Hieroglyphs,  closing,  use. . .  101-102, 152-153, 170 
Hieroglyphs,  introducing,  use  in  dating. .  64-68 
History— 

codices  containing  32-33 

dates   179, 221-222, 228-229, 249-250 

decipherment  iv-v,  26, 250 

dates  only   249-250 


281 

History— Cont  iiuiod. 

outline   2-7 

recording,  motluxis   33-36 

Hodge,  F.  W.,letlor  oft  ransmiMul   iii-v 

Holmes,  W.  H.,  ciUmI   lof, 

Hospitality,  customs   lo 

HOTUN  PERIOD   KUi 

Hunting,  division  of  spoils   9 

Ideographic  writing,  argument  for   27-28 

Ikonomatic  writing,  nature   2S-29 

Initial-series  dating — 

bar  and  dot  numbers  in,  examples. . . .  157-167, 

17(>-1S0 

plates  showing         157, 167, 170, 176, 17H,  179 

disuse   84-85,199 

examples,  interpretation   157-222, 233-240 

plates  showing   157, 167, 170, 

176, 178, 179, 180, 187, 
188, 191, 207, 210,  213, 
218,  220,  233,  235,  248 

explanation   63-74,  147-148 

head-variant  numbers,  examples   167-176, 

180-188 

plates  showing         167, 170, 176, 178, 179, 180 

introducing  glyph,  identification  by   136 

irregular  forms  of,  examples . . .  191-194, 203-207 

order  of  reading   129, 136-138, 170, 268 

position  of  month  signs  in   152-154 

reference  to  Long  Count   147-151 

regular  forms  of,  interpretation   157-191 

replacement  by  u  kahlay  katimob  dating.  84-85 

starting  point   108, 109, 113-114, 

125-126, 136, 159, 162, 203-207 

used  in  codices   266 

examples   266-273 

plate  showing   266 

used  on  monuments   85 

Inscrlptions  on  monuments— 

cycles  in,  numbering   108-113 

date  of,  contemporaneous   179, 

194, 203, 209-210, 213, 220-222 

date  of  carving,  usual   194 

day  signs  in   38 

errors   245-250 

historical  dates   179 

interpretation  33-35 

examples   156-250 

method   I34r-155 

length  of  great  cycle  used  in   107-114 

numeration  glyphs.  See  Numerals. 
See  also  Monuments;  Stel^. 
Introducing  glyph— 

lack   208 

nature   64-68, 125-127, 136, 157-158 

Inverted  glyph,  meaning   211 

Itzamna  (god),  nature   16 

Justice,  rules  of   9 

Katun  (time  period)— 

glyph  .-   68-69 

identification  in  u  kahlay  katunob   79-82 

length   02,135 

monument  erected  to  mark  end   250 

naming   80-82 

series  of   79-86 

use  of,  in  Period-ending  dates  222-225 


282 


INDEX 


Page 

Kin.   See  Day. 

KuKULCAN  (god),  nature   16-17 

Labor,  customs   9 

Landa,  Bishop  Diego  de— 

biography   7 

on  Maya  alphabet   27 

on  Maya  calendar   42, 44, 45, 84 

on  Maya  customs   7, 13-14, 19 

on  Maya  records   34,36 

Landry,  M  .  D  . ,  inves  tigations   194 

Leyden  Plate,  interpretation   179,194-198 

Literature,  list   xv-xvi 

See  also  BiBLioGRiVPHY. 
Long  Count— 

date  fixing  in   147-151, 240-245 

nature   60-63 

See  also  Chronology. 

Maize  God,  nature   18 

Maler,  Teobert— 

cited   162, 

166, 170, 176, 177, 178, 207, 210, 224, 226, 227, 231 

on  Altar  5  at  Tikal   244 

Manners  and  customs,  description   7-21 

Marrlvge  customs   8-9 

Mars-Solar  period,  relation  to  tonalamatl.  278 

Mat  pattern  of  glyphs   191-194 

Maudslay,  a.  p.— 

cited   157, 167, 169, 170, 171, 173, 175, 179, 

180, 181, 183, 185, 186, 188, 191, 203, 
205, 213, 215, 218, 220, 223, 224, 225, 
226, 227, 228, 229, 230, 235, 240, 242 

on  zero  gljrph   93 

Maya,  surviving  tribes   1-2 

Maya,  Southern— 

cities   2-4 

occupancy  of,  diagram  showing   15 

government   15-16 

rise  and  fall   2-4 

Mayapan  (city) — 

history   4-6 

mortuary  customs   12 

time  records  33-34 

Military  customs,  nature   10-11 

Minus  sign.  See  Backward  sign. 
Month.   See  Uinal. 
Monuments— 

age   249-250 

date  0  f  erection   1 79, 

194, 203, 209-210, 213, 220-222 

historical  dates  on   179 

period-marking  function   33-35,249-250 

texts.  See  Inscriptions. 

See  also  Stel^. 

Moon,  computation  of  revolutions   32 

Morley,  S.  G.,  on  Books  of  Chilan  Balam. .  3 
Mythology,  dates   179, 180, 194, 228 

Nacon  (oflScial),  duties   13 

Nahua,  influence  on  Maya   5-6 

Naranjo  (city) — 

antiquity   15 

Stela  22,  interpretation   162-164 

Stela  23,  error  in   248 

interpretation   224 

Stela  24,  interpretation   166-167 

Supplementary  Series,  absence   163-164 


Normal  date,  fixing  of   61 

Normal  forms  of  time-period  glyphs. 
See  Time  periods. 

North  Star,  deification   18 

Numbers,  expression— 

high   103-134 

thirteen  to  nineteen  96,101,111-112 

Numerals— 

bar  and  dot  system   87-95 

examples,  plates  sho-wing   157, 

167, 170,176, 178,179 

colors   91,251 

combinations  of,  for  higher  numbers. . .  105-107 

forms   87-104 

head-variant  forms   24-25, 87, 96-104 

plates  showing         167, 170, 176, 178, 179, 180 

one  to  nineteen,  bar  and  dot  forms  88-90 

head -variant  forms  97-101 

order  of  reading         23, 129, 133, 137-138, 156, 170 

ornamental  variants  89-91 

parallels  to  Roman  and  Arabic  systems..  87 

solution   134-155 

systems   87-134 

comparison   133 

See  also  Vigesimal  system. 

transcribing,  mode   138 

See    also    Hieroglyphs;  Thirteen; 
Twenty;  Zero. 
Numerical  coefficients   127-128 

Palenque  (city)— 

history   15 

palace   stairway  inscription,  interpre- 
tation  183-185 

Temple  of  the  Cross,  tablet,  interpreta- 
tion  205-207,227 

Temple  of  the  Foliated  Cross,  tablet,  in- 
terpretation   180-181, 223-224, 227 

Temple  of  the  Inscriptions,  tablet,  inter- 
pretation  84,225-226 

Temple  of  the  Sim,  tablet,  interpreta- 
tion  181-182 

Period-ending  dates— 

ending  glyph   102 

examples,  interpretation   222-240 

plates  showing   223, 227, 233, 235 

glyphs   77-79,102 

katunused  in   222-225 

nature   222 

tun  used  in   225-226 

Period-marking  Stones.  See  Monuments. 

Phonetic  writing — 

argument  for   26-30 

traces  discovered  iv,  26-30 

PiEDRAS  Negras  (city)— 

altar  inscription,  interpretation   227 

antiquity  -   15 

Stela  1,  interpretation   210-213 

Stela  3,  interpretation   233-235 

Plongeon,  F.  Le,  cited   27 

Ponce,  Alonzo,  on  Maya  records   36 

Priesthood,  organization   20-21 

Prophesying,  codices  used  for   31 

Prophetic  dates— 

examples  ----  229-233 

use   271-272 


INDEX 


283 


QuEN  Santo  (city)—  Page 

history   231 

Stela  1,  interpretation   199-201 

Stela  2,  interpretation   201-203 

QuiRiGUA  (city)— 

Altar  M,  interpretation   240-242 

five-ttin  period  used  at   165-166 

founding  of,  possible  date   221-222 

monuments   192 

Stela  A,  interpretation   179-180 

Stela  C,  interpretation.  173-175, 179, 203-204, 226 

Supplementary  Series,  absence   175 

Stela  D,  interpretation   239 

Stela  E,  error  in   247-248 

interpretation   235-240 

Stela  F,  interpretation   218-222, 239-240 

plates  showing  218,220 

Stela  H,  interpretation   192-194 

Stela  I,  interpretation   164-166 

Stela  .T,  interpretation   215-218,239-240 

Stela  K,  interpretation   213-215 

Zoomorph  G,  interpretation   186-187, 

229-230, 239-240 

Zoomorph  P,  interpretation  .   157-162 

Reading,  order  of   23, 

129, 133, 135, 138, 156, 170, 268 

Religion^  nature   16-21 

Renaissance,  commencement   4 

Rochefoucauld,  F.  A.  de  la,  alphabet  de- 
vised by   27 

Roman  system  of  numbees,  parallel   87 

RosNY,  Leon  de,  cited   27 

Rulership— 

nature   12-13 

succession..   13-14 

Scarification,  practice.   7 

Schellhas,  Dr.  Paul,  investigations.   265 

Sculpture,  development   2-3 

SECONDARY/-SERIES  DATING — 

examples,  interpretation   207-222, 233-240 

plates  showing.  207, 210, 213, 218, 220, 233, 235 

explanation   74-76,207 

irregular  forms   236 

order  of  reading   129, 137-138, 208 

reference  to  Initial  Series   209-211,217-218 

starting  point . .  76, 135-136, 208-210, 218, 240-245 
determination   240-245 

Seibal  (city)— 

antiquity   15 

Stela  11,  interpretation   230-231 

Seler,  Dr.  Eduard— 

cited   2,43,199 

on  Aztec  calendar   58 

on  hieroglyphics   30 

Serpent  numbers— 

interpretation   273-275 

nature   273 

range   32,273 

Slaves,  barter  in   9 

Southern  Maya.  See  M.\ya,  southern. 

Spanish  conquest,  influence   6-7 

Spectacle  glyph,  fimction   94 

Spdtoen,  Dr.  H.  J.— 

cited   187 

works   4 


Stel^—  |>a(re 

character   22 

dates   33.S:i-S4 

inscriptions  on   22, 33-35 

See  also  Monuments,  and  names  of  cities. 

Stones,  inscriptions  on   22 

SuPERFix,  effect   120-122 

Supplementary  Series— 

closing  sign   152-153, 170 

explanation   i.w,  idi 

lack  of,  example's   l(i3-l(')4 , 175 

position   152,2.38 

Symmetry  in  glyphs,  modifications  due  to. .  23-24, 

88-91, 128 

Terminal  dates— 

determination   13S-15I 

importance  as  check  on  calculations.. .  154-155 
position   151-154 

Textbooks,  need  for   vii 

Thirteen— 

glyphs.   96,205 

numbers  above,  expression  9(1, 101, 111-112 

Thomas,  Dr.  Cyrus— 

cited   31 

on  Maya  alphabet   27 

Thompson,  E.  H.,  investigations   11 

TiKAL  (city)— 

Altar  5,  interpretation   242-245 

antiquity   127 

history   15 

Stela  3,  importance   179 

interpretation   178-179 

Stela  5 ,  interpretation   226 

Stela  10,  interpretation   114-127 

Stela  16,  association  with  Altar  5   244 

interpretation   224,244 

Time— 

counting  backward   14(>-147 

counting  forward   138-146 

glyphs  for,  only  ones  deciphered   20, 31 

lapse  of,  determination   134-155 

expression   iWi-i'A,  105-107 

indicated  by  black  glyphs   251 

marked  by  monuments          33-35, 249-250 

method  of  describing   46-48 

recording   3.3-.36 

use  of  numbers   134 

starting  point   G0-(i2, 113-114. 124-125 

See  also  Chronology. 
Time-marking  stones.  See  Monuments. 
Time  periods- 

full-figure  glyphs   (i7-(;8, 188-191 

plate  showing   188 

head- variant  glyphs   67-74 

plates  showing         167, 170, 176, 178, 179,  ISO 

length  •-   62 

normal  glyphs   r.7-74 

plate  showing   157 

omission  of   128 

reduction  to  days   134-135 

See  also  Cycl'e;  Great  Cycle;  Haab:  Ka- 
tun; Tonalamatl;  Tun;  Uinal. 
Tonalamatl  (time  period)— 

graphic  representation   93 

interpretation   254-266 


284 


INDEX 


ToNALAMATL  (time  period)— Continued.  Page 

nature   41-44,265 

relation  to  zero  sign   93-94 

starting  point   252-253 

subdivisions   44 

texts  recording   251-266 

essential  parts  of   265 

use  of  gl>T)h  for  "20"  with . .  92, 130, 254, 260, 263 

used  in  codices   251-266 

plates  showing   254, 2G0. 262, 263 

used  in  divination   251 

wheel  of  days   43 

See  also  Year,  sacred. 

Translation  of  glyphs— 

errors   154-155 

methods   134-155 

progress   250 

Tun  (time  period)— 

glyph  -   70 

length   62,135 

use  of,  in  Period-ending  dates   225-226 

TuxTLA  Statuette,  interpretation        179, 194-196 

Twenty— 

glyphs   91-92,130 

need  for,  in  oodices   92, 130 

needlessness  of  ,  in  inscriptions   92 

use  of  in   254,260,263 

Uinal— 

days   42 

first  day   53 

glyph   94 

glyph   70-71 

length   45.62,135 

list   45 

names  and  glyphs  for   48-51 

U  Kahlay  Katunob  dating— 

accuracy   82 

antiquity   82-85 

explanation   79-86 

katim  sequence   80-82 


U  Kahlay  Katunob  dating — Continued.  Page 

order  of  reading   137 

replacement  of  Initial-series  dating  by . . .  84-86 

UXMAL  (city),  founding   4 

Venus-Solar  period— 

divisions   31-32 

relation  to  tonalamatl   32, 277-278 

Vigesimal  numeration— 

discovery   iii 

explanation   62-63, 105-134 

possible  origin   41 

used  in  codices   266-273 

Villagutiere,  S.  J.,  on  Maya  records   36 

War  God,  nature   17 

Weapons,  character   10-11 

World,  destruction,  prophecy   32 

World  epoch,  glyph   125-127 

Worship,  practices   19-20 

Writing.  See  Hieroglyphics;  Numerals; 
Reading. 

Xaman  Ek  (god),  natme   18 

Yaxchilan  (city)— 

lintel,  error  in   245-246 

Lintel  21,  interpretation   207-210 

Stela  11,  interpretation   176-177 

Structure  44,  interpretation   177-178 

Year,  Sacred,  use  in  divination   251 

See  also  Tonalamatl. 

Year,  Solar.  See  Haab. 

Yucatan— 

colonization   3-4 

Spanish  conquest   6-7 

water  supply   1 

Yum  Kaax  (god),  nature   18 

Zero— 

glyphs   92-95,101-102 

origin   93-94 

variants   93 


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I  ^111^^^^^^  INSTITUTE 
'  3  3125  01450  8069  ' 


